 I figure what I'll do is I'll first I'll take questions and answers from the review. I have a second review that I used to give out. It's not quite as good because it's based more on the Alberta curriculum, remember the Alberta questions are a little tougher, but I do have a PDF of that and a handwritten solution key. I'm going to put both of those online tonight, and when I email you guys, I'll include a link if you want those as extra practice, okay? And then I'll also try and give you some generic hints about the test. I don't think you're going to find too many surprises on the test, so specifically the last big mega quiz that I gave you, that there probably is about 70% of the test, maybe even higher, okay? So if you understand how to do that, you're good. What's not on the big mega quiz? Simplifying factorials when you have one on top of the other, okay? There's also some questions from this review that I'm not hugely fond of, but it's better than the other one that I used to give away. So let's start out by saying, are there any questions from the review that you would like me to go over, ask away my children? Yep. 34. Can I get you in favor and shut that door? And Jimmy, could you get me in favor and shut that door? And then let me get Jasmine going on the test and I'll give Lorenzo a copy of the review. So number 34, there's absolutely going to be one of these on your multiple choice section. I'm going to give you some kind of a factorial expression to simplify. And I'm going to be honest, I think the one that I give you on your test is actually even a half-step nastier than this one, okay? Also because some of the questions on the multiple choice, you're going to find it really, really easy. Oh, I'm just multiplying it. I'm done. Yeah. Some of them are going to be that easy, but some of them are going to be trickier. I'll also give you some hints about the written section as well. But number 34, here's what I would do. First of all, do you notice, Shanna, there's no factorial on the N there. I'm just going to keep dropping it down and see what happens at the N. So I rewrote the N. I looked at these two and I said there's nothing, I looked at these two. There's nothing that lets me cancel out a factorial symbol. But what I can try and do is expand one of these and tell stuff cancels. What's bigger, N plus one or N minus one? So I'm going to expand that. I'm going to say that's N plus one. What's one less than N plus one? What's one less than N? And I'm going to stop right there and add my factorial sign because that's what I had in the denominator. So now I can cancel out the factorials. What I have is N times N plus one times N. If I tidy that up, I have N squared times N plus one. I didn't see that answer anywhere. Oh, you know what they did, Shanna? They multiplied and got rid of the brackets, didn't they? Which is the correct answer? D. D as in dog, as in the one I circled. D. Yeah. Oh, I think he said B. Is that okay? There's one question somewhere in the review I can't remember where, where it has something like this. I'm just making this up. N plus one factorial and then it has an N factorial in brackets squared. I don't deal with that. What I do right away is I treat that as N factorial N factorial because isn't that the same as N factorial all squared times itself? And then usually they'll have a second term up top here like an N minus one factorial. I would mentally just kind of divide it into two mini fractions and simplify each of those first and then go top times, top bottom times, bottom and see what I get or something like that. There is one like that somewhere in your review. I can't remember where, but I know it's there somewhere. What number? Did you find it, Jeff? Oh, okay. Next. 11. By the way, are you guys able to access my solution key? Okay. There's a mistake on the solution key. So all of you look up. The answers are right on the back of yours and I already paid the dollar out to Courtney. So those of you that are wanting to claim the dollar bounty, you're out of luck. For some reason on the handwritten one, I picked C15 for number six. It is B14. I counted wrong on my fingers. Go figure. No comments. Thank you. I heard that. Okay. Anyways, number, sorry, 11, 11, 11, okay. How many six-digit numbers greater than 800,000 can be made from those? I said, well, six digits and this looks weird. I fell back to fundamental counting principle. First of all, I said, okay, I'm going to have one, two, three, four, five, six. If I'm greater than 800,000, that has to be an eight. How many ways can I choose an eight from here? One. Then I said, now this is a bit different because in the previous questions, I never gave you the same number twice in a row. Here I have two ones and three fives. Here I have two ones, oh, begins with one, one begins with one, and three fives. You know what? I said, that's a word. How many letters in that word grand total, five factorial over how many ones, how many fives, that's how many there are. This was tricky. That, by the way, that would be considered one of the nastier combinatorics questions you would see. That was because unlike all the other ones where I only gave you certain numbers to pick from in that scrabble tile analogy, here I had more than one of the same scrabble tile. The permutations with repetitions, the Mississippi one or Tawasin or whatever examples that, oh, when we found the permutations of your last names, first and last names, that one. Next, 15. I like number 15. I like number 15. Number 15 is a nice question. It's funny, as soon as I said that, I heard about 10 more people start turning pages. It was quiet, quiet, and as soon as I said, I like number 15, I said, turn, turn, turn. Follow along, boys and girls. Are some X's in the denominator? Are some X's on the top? Is it possible that when they get multiplied together, somewhere along the way, they could all cancel? That's the constant term. When? I don't know. Let's figure it out. To figure it out, Kayla, I'm going to ignore the two because that's not going to change when the X's cancel, and I'm going to ignore the negative. That's not going to change when the X's cancel. I'm just going to look at the actual X's that are on the top and the bottom to figure out when they cancel, and then I'll take it from. Actually, all this wants to know is when they cancel, so I'll be able to stop there. I won't even have to actually figure out the term. What's my great big exponent here? It would be 8 of the 10th, 8 of the 9th, B, 8 of the 8th, B squared. I think I'll be able to figure out the pattern from three things. Okay, let's keep going here. What I think I have here is 1 over X squared to the 10th, because A is that thing, but I'm ignoring the two temporarily. Here I have 1 over X squared to the 9th, X cubed to the 1. Is that okay? Here I have 1 over X squared to the 8th, X cubed squared, and now I'll start to spot the pattern. How many X's on top here, none? How many on the bottom? Okay, this is an X to the negative 20, there's 20 on the bottom. How many X's on the bottom here, 18? How many on top, three? There's 15 on the bottom, that's the same as X to the negative 15. Bet you we're going up by fives, but let's see if we get a negative 10 here. Oh, I have 16 on the bottom, 6 on the top, 10 left on the bottom. Okay, negative 20, negative 15, negative 10, negative 5. You know when I have zero X's? What term number? Fifth term. I hope that's what I said on my answer key, I think I did. Yay. Next. Okay, while people are pausing then, if you want to look at your review and go to number one, I'll tell you which questions I really, really, really, really, really, really like. Let's see. I like number one, two, four is good, seven. Can you all look at number eight for a second? You know how I know that this is a permutation and not a combination? It's a trigger word for that, arranged in English and arrangement is an ordering, right? Rearrange yourselves. What I really mean is don't change the group, but change the order, okay? So arrangement, that's one of my trigger words. So here it would be 8p8 or 8 factorial, sorry, 7p7 or 7 factorial. Number nine, so simplifying a factorial, oh, this is the one I was trying to think of so that n factorial all squared on the bottom, I would break that up into n factorial and factorial. And then mentally, I kind of divide the fraction in half, simplify each half and then kind of see what was left. 13, but make sure you can handle 13 if it was a written question as well. Now it's multiple choice, so you guys know how I did it, right? What does it say? What did I do for number 13? I just tried the answers, multiple choice, don't waste your time, try the answers. Will I give you that as a multiple choice? Everybody shake your head no. Will I give you some kind of a factorial equation that's always written? Absentively that's on your test. Eventually, 15 is good, 16 is good, 16 will be a written, though, okay? 18 is good, so 19 is good, 19 is different from 15 because 19, it's nice regular rectangle, there's no overlap, so you can use the shortcut of permutations and choose. There'll be one something like that as a multiple choice and then on the written there'll be one we have to use Pascal's, okay? 20, 22 is good, there's going to be something sort of like number 23, what I mean by that is there's going to be some question that you have to use the fundamental counting principle and ask yourself how many choices do I have for the first blank? How many choices do I have for the second blank? How many choices do I have for the third blank? How many total choices? I thought I was doing pretty good but apparently I lost one member of the audience there, okay? So this one was license plates, I don't know if it'll be license plates, I'll be honest, at least one of them is going to be given X number of digits, how many four digit numbers or four digit odd numbers or four digit even numbers or three digit odd numbers. Please remember that you can't begin a number with what? Zero, and I guarantee I'll put zero in the scrabble bag to make sure to test you on that, okay? 25, again make sure you can find a given term of a binomial expansion, 26 but hopefully that was obvious, 29, how do I know that's 7p3 and not 7c3? Arrangements, okay, that's the English word, there's others like if they start talking about positions, a vice president, a president and that's clearly a permutation as well because it matters when you get selected but if you're not sure, one of your triggers Shana, I see the road arrangement, that's permutation, I've already said a bunch like number 31, so, but yeah 31, 33 is good, how do I know number 37 is a permutate, well 37 is a permutation but it's a word, how many r's are in this word in number 37, 4, how many g's are in this word, 4, how many y's are in, do you see what I'm doing by the way, I'm taking the first letter of the colors, right, this is a word, now it's an arrangement, yes, see the word arrangement Regan, so it's a permutation but it's got repetitions, so this would be mixing up the word r, r, r, r, g, g, g, y, y, y, y, which would be 12 factorial over 4 factorial, 4 factorial, 4 factorial, whatever the heck that is, I don't know, 38 is great, that's what I would get, some kind of a fundamental counting principle count of the question, 39, really quickly right now, what's the answer to number 39, don't say 9, 10, right, so 41 I've already said you know when something like that on the written, where you're either missing lines or you're sharing lines, you've got overlapping lines or something, 43 is I like except it's going to be a written and it's going to be first four terms and that one's too easy because the x is all by itself, I'm going to put something in front of each variable, in fact you know what, probably one of the variables might even have an exponent on it, it might be like a 5x squared minus 2y or something like that, okay, 44 makes a great written question, 46 is great, in fact I'll even go more specific than that, look at number 46, is it a word, everybody say yes, does it have more than one of the same letter, so it's one of those one, it's going to be number 3, 4, 5, don't think it's 2 and that's not a surprise because I've told you the multiple choice is going to follow the exact same order that I taught you, number one I guarantee is fundamental counting principle, probably number two as well, probably number two though might have some kind of restriction, number three is going to be a straight permutation, number four is going to be a permutation with repetition, maybe number five somewhere in there, same with 48, a lot of these start to get repetitive so I'm not repeating myself over and over and over, we nuked number 54, Mitch can you cross out number 54 please, so something like 57 is a good example of here's a fundamental counting principle but with some type of restrictions, in this case two odd digits followed by three even digits repetitions are not allowed, okay, five blanks and carefully think how many choices for each blank, right, okay, written section, so some kind of a factorial question, so something like number three but I might give it to you in choose notation or permutation notation as well and I will do one of these in just a second because somebody has asked, absolutely number five, some kind of a committee question where I say okay you got committees or cards, I don't know I can't remember which one I typed in, I typed it up on the weekend so it's either going to be you know how many ways are to get three spades, two hearts and four others or girls and guys or some kind of a break-up that way and there will also be a part B where there's an at most or an at least, at least three hearts or at least two males or at most two males which would include two or one or zero, list your cases boys and girls, hang on what does or mean add, what does and mean multiply, someone in one of my classes said it wrong, might have been you I can't remember, it was you, oh yeah I do it as a memory here okay six again and seven algebraic solving factorial type equations I'll do a couple of those in a second so nine is again classic committee question fact nine is nice because there is part A is just committee that would be thirty choose three part B are they talking about specific positions that's a permutation that would be either drawing three blank lines and going thirty choices twenty nine choices twenty eight choices or that's also the same as thirty P three on your calculator and then part C is an at most at least I think oh no part C is one boy two girls so division that's also a nice kind of a written question I already said number 11 except I said to you it's going to be four terms and it's going to have a coefficient in front of the X and the different number in front of the Y probably maybe even exponent 12 and 13 are all good 14 15 is good so 15 is an example of a combinatorics question where I've given it to you in fact in choose notation first and then you're going to solve the factorial equation so someone said Mr. do it could you do one of those how about I do you want me to do number three is that good okay hearing no argument isn't this like number 15 isn't number 15 is solving a factorial equation is it or isn't it I'm going from memory but I thought yeah I think this one's harder is it not got more stuff in it this one okay I'll do 15 as well but I don't mind doing two let's do this one first though okay Kayla first thing I would do by the way is see that three factorial no it's a six like I would right away say let's I can't do anything with the algebraic factorials but the number of factorials I can evaluate those and that looks a little cleaner so I would say to myself this is n factorial all over n minus two factorial times six equals five and then to be honest I would cross multiply part of this I would move this six over to this side by multiplying I would solve that equation you okay with how I got there okay need to deal with this which one's bigger n or n minus two that's the one I'll start to expand all right it as n one less one less ooh stop there because now the denominator just appeared you okay with that can I cancel is it factored yeah so I can in fact here's the equation you end up with n times n minus one equals 30 now what yes we'll get rid of brackets distribute if you want the fancy word you'll get n squared minus n and then it's a quadratic so I'm gonna minus the 30 over to this side as well make it equal to zero I know you know what to do but I saw a few other blank eyes by the way that's why I'm continuing okay this is gonna be factor n minus six n plus five equals zero and you get six and negative five and are we done can't have a negative factorial because you can't have negative five objects okay yep okay what is three factorial a more specific please in your head with other calculator you want to be wearing your visor a little more often I think maybe a mouth guard or get that helmet checked okay five okay you okay with that so what I said Mitch is often there's gonna be a numerical factorial question here an expression here get rid of that like do that math if there's a fact I think there's one somewhere in the reviewer to look at four factorial and you'll notice on my solution key I didn't even write I put a 24 there right away looks better okay especially two factorial is the one that shows up the most what is two factorial just plain old two so that one you can even just just erase the exclamation mark okay okay you'll count 15 or do you want me to do 15 I can do it if you want me yeah I have no memory of what that one looks like but you're saying that one looked uglier oh no not 15 you're talking about it I did 15 already oh in the written section oh I was going wait a minute in the written section oh that there sure give you formula sheet in front of you can you tell me from your formula sheet what is npr equal to if I translate that here isn't that n factorial over n minus 2 factorial equals 90 and by the way can you see we just turned it into this question now except instead of a 5 I got a 90 then you'll get m squared minus n minus 90 equals 0 for what it's okay you're ready look up here's how you can check your answer if I'm using a permutations only works for this type we're using a permutation the answers that have to work the numbers when I'm making this up the numbers that I use here they have to be gettable obtainable by multiplying two numbers that I want apart I'll tell you what I mean by that 9 times 10 would work 8 times 9 I could get 70 if I put a 72 right there there would also be an answer so I think there's one question in your review where there's a 42 right there right away I know the answer is six or seven because 42 is six times seven but there's only certain numbers that I can plug in that won't give you decimal answers can we have decimal answers no because you can have 6.8 objects okay so when I'm making these up and choose to well I could go like this two times three I could put a six there three times four I could put a 12 there four times I could put a 20 there five times I put a 30 there so if you look when you get one of those for example if you saw oh you saw 56 there 56 is what times what you know what the answer is either eight or seven tell you that right now that's how I made it in fact I'm pretty sure it's always the bigger one if you play around with it for a while it's probably eight but you can't just write the answer you got to show me work but I've given you kind of a built-in air check now that does not work for the weird generic factorial ones where they've already given it to you in factorial notation that probably doesn't work there although I notice 30 is six times five maybe there is something to this well no 10 is not 10 is not okay so it doesn't work for that but I've never showed kids that until the very end I just for some kids spot it okay any others you would like me to do yeah multiple choice 12 yeah I'm putting this in theory online yeah in theory online the only concern I have is every once in a while it hasn't worked right I'm batting about 90% right now but that 10% could show up one day at the wrong time and for some reason either the server or the video service or what I've had days were for 24 hours I couldn't upload the video we're doing number 12 okay got the review look in front of you can you read number 12 out loud to us and nice booming voice pat voice pat in the front row here I don't see that at all here's what I see I see a word you see what the answer is it's gonna be 10 factorial over 4 factorial 3 factorial 3 factorial and it's not a coincidence that there's 10 letters and 10 people if they'd said nine people you guys don't have the skills to do this question in fact they would be fairly tough that's why I don't remember but I said quite often what we're gonna do is we're gonna turn a word problem into a word there I think the answer is D I can't remember I was a bee okay oh D is 10 factorial probably that'd be one wrong answer to put on there also probably one of the other answers is like ten choose four or ten choose three because that might be something else kid might try but it's a word okay next yep 53 and Pat I already kind of gave them the I like these questions routine so you have to watch the video or ask your peers so I probably have to do 52 well let's look at the whole thing at least one car Justin that means one car or two cars or three cars yeah I need more room one car or two cars or three cars or four cars what does or mean and I drew my little bucket I said in this case although they've talked about cars trucks and motorcycles here the only thing they're mentioning is cars so I went with cars and others how many cars are there 12 how many others are there 13 and the reason I can do that is they haven't specified anything about trucks or motorcycles so I guess they're treating this one group can see now what it's gonna be it's gonna be a 12 choose 1 13 choose 3 that's the first expression 12 choose 2 13 choose 2 that's the second expression 12 choose 3 13 choose 1 12 choose 4 13 choose 0 let me show you my work for that question and then I went to my calculator I wrote down each of those and just add them together I didn't type this all in in one line I type that in first wrote down the number and then hit second function enter and change the 1 to a 2 and the 3 to a 2 enter change the 3 to a you just kept retyping it that way is that okay that was a bit tricky I had to think about it for a second now I went what I actually did here Justin is I treated it like cards initially I was like what the heck I said wait a minute if they had said at least one spade I wouldn't have a separate group of diamonds a separate group of hearts in a separate group of clubs I would have gone spades and others I don't care about the other distributions so you're ready here's the other question preview of coming attractions not on the review but since you guys came to the tutorial you guys get the big bonus oh hang on I'm in the wrong unit no wonder I couldn't find it thank you captain obvious here we go no laughing if you have your workbooks here now if you don't that's fine but if you have you can just write this down but for what it's worth I really like page 413 example 4 I really like page 413 example 4 page 413 example 4 is a nice question or if you want some more examples similar to that I'm thinking that number 10 would be examples of said question the only thing I would do in 10 a just because it annoys me what letter did they put their Lawrence we always called that a B I would just overwrite it like that so I wouldn't confuse myself otherwise just why make it take the risk of making a silly mistake back to the tutorial Mr. Dewick will you show us how to do one of those actually no I'm gonna say look at your notes and figure it out that's part of the test and see who's but I told you you're gonna see okay going backwards where instead of saying here's the binomial find the seventh term I'm gonna give you the seventh term part of the binomial and find the missing part of the binomial okay I told you about the written so let's talk a bit more written question section is gonna have I believe the first question on the written is I give you a binomial and I say write the first four terms out hang on don't go there oh yeah first question I give you some kind of a binomial I say right the first four terms second written question is a pathway third written question and I've told you this already is one of those committee card at most at least more than guys girls or spades clubs one of those fourth question is solve the factorial then I have a card question how many seven card hands have at least three read or something then I have the one that I just told you about that I like that I like that I like that I like and then the I also have a fundamental counting principle kind of a question with some kind of a restriction for example if I give you a word but I say certain letters have to be together I think we did one where the word was kitchen and the question said the T and the C and the H had to be together so all I did is I pretended that was a one weird looking letter scrabble tile shhh TCH and then I had a K and I and E and N so I only had five scrabble tiles oh but how many ways can I mix up that scrabble I'll let you think about I just told you every one question on the written the one I'm still saving so what about the multiple choice pretty straightforward in fact I would say if you work your way through the review there will be no surprises on the multiple choice and on the written I think the only thing that's on the written that's not in the review somewhere was the one that I said about 30 seconds ago I like I like I like I like I like but that was in your homework so I feel okay you should find this a pretty easy test to get a decent grade on pretty tough test to get perfect any others you want me to do it's a short unit yeah sure can you find one like that for me they are if you're never late sure there is one I think I said I think there is one of these on the written or it's either on the multiple choice or on the written I might have done both I can't remember but you're definitely gonna see one of these tomorrow so sure you have a formula sheet in front of you Lawrence get one because this may that may be why you're having such a tough time with these have I kind of gone on a rant about why you should have your formula sheet in front of you during this unit several times not your head okay going okay the formulas for this unit are about two-thirds of the way down find them okay find the one that has a T for term in it okay that's the one so the first thing I would do is I would carefully copy this one out if I was doing this on the test is that correct okay what term do they want me to find here so I want term 10 that's our abbreviation what term I may ask you again not to make fun of you but to illustrate upon what term for that to be a 10 what does K have to be can we guys he's got to learn this okay you understand why it has to be a nine what do I want term what so for that to be a 10 what does K have to be why well because this is the equate the formula has a K plus one if I want the K plus one to be a 10 the next thing we run into what's n here no well that n is somewhere here Pat what is it 10 okay so n is the exponent oh are you saying that n stands for a number really that's how you remember it wow you're clever Lorenz what's a the first part of the binomial B is the second part of the binomial okay so you have to be able to find those it's not on your foot this is on your formula sheet but you have to know what each of these you have to know what each of these means once you have that it's plug-and-chug are you ready what's that choose what's that what's that to the power of what's that in your head please no calculator so what you're going to go on your calculator is ten choose nine times two to the I guess two to the one so I can just go times two times negative one to the ninth which would be negative one I think but can you see if there was actual numbers there I could follow the numbers as well they're on the list of episodes you can have it or just drag them onto your laptop and double-check double-click on them to see if they play they might not if you don't have a different media player installed besides the windows media player but I can fix that oh I did do I gave you being proactive that's the way to do this for me I think you have to type it like I lost my calculator oh the people at home that last conversation I was just giving something to a teacher if you're wondering what the heck that was the people in the room figured it out you're gonna go ten choose nine times two to the one but if there was a different exponent there I put that there times for a negative number I always put it in brackets just to be safe to the ninth but if there's a different number there that would be a different exponent there and I get this negative 20 that's the coefficient yes because there's a negative right there and it's not going to vanish it's ten choose nine times two to the one negative one to the ninth power is negative one if they're even the negatives would pair up and cancel out if the exponent was even oh sorry right that negative doesn't cancel I don't know I just typed it all I did all the numbers yes and then I have an x to the one I'll just write x I have a y to the ninth but where is the y so you do that okay you'd lose marks definitely because it's nowhere it's look it's not on the top then you wouldn't get perfect I glare at you and be going oh your generation sucks at fractions no I've pushed you into mediocrity during the trig identities unit please we became mediocre at fractions I can almost tolerate it now almost any others 38 Jasmine what block are you yeah can you put it on top of block D for me please thank you 38 oh nice question how many odd three-digit whole numbers are there you know what I'm gonna go fundamental counting principle because this is one of those odd or even number type things okay what makes an odd number an odd number okay it ends in a one three five seven or nine how many choices do I have for that last digit then because that's the restriction I've told you I don't care where the restriction appears I always do it first does it say I can repeat or does it say I cannot repeat doesn't say I cannot repeat then I can okay so let's suppose I picked a seven back in the bag shake the bag up how many digits are now in the bag ten how many choices do I have for the first number though why nine not zero and it doesn't say repetitions are not allowed so back in the bag shake the bag back up how many do I have sitting in the bag it's gonna be 50 times nine 450 nice question some good thinking there tricky ish but not so hard that I would consider that anywhere near on fact I'd expect most my kids to get that but lots of potential to make sloppy mistakes and need to gently yell at you and love and say fix those mistakes you don't yell at us and love Mr. Duke well I do yeah any others yeah 35 this one was kind of tricky I would probably consider this a b-plus maybe in an a-minus level question Shannon so good question okay what's my great big exponent now the problem here is they didn't tell me which term to find see if they told me it was that I'm making this up third term then I would go tk plus one equals n choose k a to the m minus k b to the k if they want the third term k is two and I bug a problem is I don't know when that appears would you say my big exponent was so I think it's going to be a to the six then a to the fifth b then a to the fourth b squared and a matches are there's are there's no exponents inside here to make this pattern change a little bit you know what what term number is that Shannon it is I just guessed third that was a fluke by the way you know what this question wants me to do it wants me to find term three are you okay with the rest of that now are you okay using this equation or do you want me to do it I can do it if you want right again key is k is two and is six a is to a b is negative 3b I ignored the two and the negative three just to find out when the term occurred because the negative two and the negative three aren't going to change the exponents that's why I just wrote a to the sixth a to the fifth b I didn't care about the chooses but now I do because they want the actual term is that okay Justin you had a question written 12b written 12b oh very nice I would consider this a nice upper level question probably what I would do though is well no this was on an exam so this was fair game so be we want four students grand total from seven boys and five girls but it's got to have a female president a male vice president and then two other members chosen from the remaining students I'm going to have female president male vice president two others we don't care about well sorry we care about them we want to be on the committee we don't we don't care how they're selected how many ways here's my restrictions I'll do them first how many ways do I have to choose a female vice president how many females are in the group I got five ways to choose a female vice president order clearly matters here because they want they're talking about positions okay how many ways to have to pick a male vice president seven do they care whether the remaining two are boys or girls or anything like that at all nope then you know what how many kids do I have left to pick from if I picked one girl and one boy how many are left then there it is 35 times 90 whatever the heck that is I don't know as soon as I did that ah now I see it again nice little question good little extension okay there is a combination of permutations and the comp well a permutation and a combination count cool you know I think I might have done this one wrong actually you know why I just thought about this by the way I was spacing out going wait a minute something's bugging me here I then you raised your hand and brought me back if I did that and that that's a permutation that's saying the order that those last two kids get picked matters and it doesn't what I should have done is I should have said how many kids are left Justin 10 choose to who cares when they get picked just pick any two that's what it should be yes and then it's 35 times whatever the heck 10 choose to is and I have no idea what 10 choose to is that makes more sense to you otherwise I would be counting if I've done it 10 times 9 I'd be counting Billy and then Jennifer as the same as Jennifer and then Billy I'd be counting this different events and they're not so yeah there's an example of a permutation combined with a combination that was that was a considered a fairly tough question though so if you're finding like I might not have got that right don't feel bad and hopefully you will if you see one like that I would probably put this as a multiple choice myself although this wasn't written in 2003 so fair enough anymore any others I'm good to go for a bit still one and down okay there with me for a moment when I hit stop and save