 So, an important branch of mathematics is called combinatorics, and it deals with the topic of combinations and permutations. So, let's talk about permutations first, as they're a little bit easier. Suppose I have a couple of choices I want to make. So, for example, I want to choose a movie to see, and then I have to determine what time I want to see it, or maybe I'm ordering an entree, and I have to figure out what the side dish is, or maybe I'm choosing a list of courses, and each course has a couple of different times that it's offered in. So, the starting point of combinatorics is the fundamental counting principle. Suppose I have m ways of making the first choice, and n ways of making the second choice, then I have a total of m times n ways of making the two choices. And a very convenient way of thinking about this is to imagine that each choice corresponds to one entree in some sort of a table. So, going back to the movie and showtime example, I have my choice of movies, and I have my choice of times. And let's say that I have a choice of five movies at the theater, and then I have a choice of, say, three showtimes. So, I have three choices of movies, five choices of times, and the fundamental counting principle says the number of ways I could pick a movie, and a showtime is five times three is equal to fifteen. Now, an important concept is the distinction in mathematics between what is a permutation and what is a combination. The two are very easy to get confused, and it's important to make sure that we know which one we're dealing with. And in general, one way to tell is that if it makes no difference where we record a choice, then what you're dealing with is a combination. On the other hand, if recording a choice in a different place changes the choice that we've made, or in some cases might actually be impossible, then what we're dealing with is a permutation. So, for example, let's consider our movies and showtimes. So, I had my choice of five movies, I had my choice of three times, and I might choose a movie, The Avengers, for example, and I might choose Time, for example, 7.30 p.m. And here's the important thing. Once I've chosen, once I've made my selection and placed it in a spot, there's only one place that that selection can go. It doesn't make sense. If I switch them, there is no movie called 7.30 p.m., and certainly if I try to see the movie 7.30 p.m. at the time, The Avengers, I can't do that. That selection doesn't make any sense. And in this case, it's actually impossible to switch where we record the choice. So, if it's impossible, then what we're dealing with is a permutation. Well, how about those meal combinations? So, for a combination meal, I've chosen three entrees, five sides, and six drinks. And first off are these combinations and how many different meals are actually possible. So, again, our principle here is if I can alter where we write a choice without changing what it is, what we're looking at is a combination, otherwise we're dealing with a permutation. So, let's make a few choices. So, I have my choice for entre, my side, and my drink. So, I have a cheeseburger fries with a coffee. So, to answer the question whether I'm dealing with a permutation or a combination, the thing I want to answer, can I switch where I write down a choice? So, let's actually do that and see what happens. And so, now for my entre, I want fries. For my side, I want coffee. And for my drink, I'll have a cheeseburger. And that doesn't make sense. That's actually not allowed. I can't have a cheeseburger as a drink. I can't have coffee as a side. And I can't have french fries as my entre. So, what we're dealing with is not a combination because it does make a difference. And so, I have a permutation. And so, that means I can apply the fundamental counting principle without really any further comment. So, I have three choices for entre, five choices for sides, and six choices for drinks. And so, the number of meal choices I could make, three times five times six, is going to be 90 different combination meals. Well, they're not combinations, they're actually permutations. So, I have 90 different permutation meals that are possible to have.