 But counting rules. Counting rules are a way or a method of putting things or counting how many number of ways you can do things. The first one that we're going to look at is the multiplication rule. But multiplication rule tells us how many number of ways can we do things. We can do things n1 times n2 times ni ways. Okay. What does that mean? Let's look at an example. If I have three packs for restaurants, six movies, how many different possible combinations can they be? Or how many number of ways can I visit all of them? To visit all of them, we need to multiply the three packs with the three restaurants with the six movies in order for us to find the number of combinations. So it will be three times four times six, which will give us 72 ways. So it means we can go to three packs for restaurants, six movies, and 72 ways that we can do. There are 72 ways that we can do that. What we're going to look at is the factorial. Also the factorial tells you how many number of ways you can place things or do things. So with factorial, there is a exclamation mark to the number. And that just says it can be n times n minus one times n minus two times n minus three times until you get to two times one. In an example, suppose I have four books that I need to take out from the library. How many number of ways can I take those number of books? So there can be four factorial ways. It means four times three times two times one, which will be 24. Number of ways that I can take those books from the library called the permutation rule. The permutation as well, it tells you how many number of ways can I do things. But yeah, we look at if there is order or priority or preference of doing those things. So if I have a permutation formula, which looks like that, it's m, which has a total number p with represented permutation of the number of ways which are those x equals m factorial divided by m minus x factorial. Remember the factorial? The exclamation means we're moving from high to the lowest multiplication. So how do we then calculate this? If I need to select a president, a secretary to form a part of the committee from a 12-person committee. And I need to select the president, the secretary, and the treasurer. And yeah, there's a preference because I'm told there is an order that I need to select a president, the secretary, and a treasurer. How many possible arrangements can they be? So how many number of ways can I select all these three people? To select those three people is 12 p, 3, where 12 is the total number of committee members, and 3 is the number of positions that I need to be selecting. 12 factorial divided by into bracket 12 minus 3, which our m is 12, and our x is 3. And we substitute into that formula and we calculate. 12 factorial will be 12 times 11 times, will be 12 times 11 times 10, until times 2 times 1, divide by 12 minus 3, which is 9, it will be 9 times 8 times 7 times, until 2 times 1. And that will give you the top part, where 12 factorial will give you 479 million and 1600 divided by 362,880, which is the 9 factorial. And that will give you 1,320 ways of selecting those three positions. There are 1,320 ways of selecting a president, the secretary, and the treasurer. It's called the combination, and combination it is where you are not told the order or the preference of how things needs to be done. How do we do that? We use the formula ncx, which is m factorial divided by m minus x factorial times x factorial. We select three people out of 12 people to form a committee, how many possible arrangements? This is the same as what we had in previous. Remember in the previous, we were told which positions, now here they are not telling us which position they just need to, we just need to know how many three people can we select from these 12 people. And to do that, substitute our m is still 12 and our x is still 3, but the formula is different because it's a combination there was no order or preference. 12 factorial divided by 12 minus 3 factorial times 3 factorial, like this. It's 12 factorial divided by 9 factorial times 3 factorial, which is 12 factorial 12 times 11 times 10 times 10 times 2 times 1, divide by into bracket 9 times 8 times 7 times 2 times 1. So you go until 2 times 1 times into bracket 3 times 2 times 1 close bracket. And that will give you, if you simplify all of it, it will give you those values 4079001600 divided by 2,1772800. If we simplify it, it gives us 220. So therefore, if we have to select three people from 12 committee members to form a committee, then there are 220 ways of selecting those people. The difference between the two, combination and permutation is permutation, there is an order of preference, combination, there is no order of preference. Thank you.