 In this video, we provide the solution to question number four for practice exam number four for math 1030 In which case we have to evaluate the product of 10 permutation four times 10 Combination four divided by four factorial. So let's go into the definition of what these things here mean What is 10? Permutation four even mean So the idea there is you're gonna get 10 times 9 times 8 times 7 so starting at 10 You fall downwards four times, okay Then you have a four factorial on the bottom four times three times two times one And then with a combination There's a couple ways you can do it you can treat it like it. Well, I'll just write it out as a factorial here So you're gonna get ten factorial ten times nine times eight times seven times six That's a six there times five times four times three times two times one And then you're gonna sit on top of four factorial again four times three times two times one And then you also are gonna end up with a six factor where six come from six is ten minus four So you're gonna get six times five times four times three times two times one And so now we want to cancel and simplify this thing This is gonna in fact be an integer when we're done So the six factorial will cancel off with this very quickly and now we're gonna search to cancel out the other Things notice that three times three is nine that cancels with that nine right there Four times two is an eight four times two is an eight So let's see what we have left over So things that didn't get cancelled out you're gonna get ten times nine times seven times ten again times seven again For which we end up with you know ten times ten of course is one hundred Times that by nine that makes it nine hundred and then seven times seven is forty nine And then if you take nine hundred times forty nine really we just have to do nine times forty nine and slap on two zeros at the end So honestly any answer that doesn't have two zeros on it. We can already eliminate it Okay, but anyways if you take nine times forty nine that's gonna give you four hundred and forty one slap on two zeros We get that the answer is forty four thousand one hundred so the correct answer here would be e