From the course: Preparing for the GMAT

Permutations

From the course: Preparing for the GMAT

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Permutations

- [Instructor] So when we count things, it's a permutation if one order of the arrangement counts separately from another order of the same arrangement. So in this video we'll look at a few permutation questions, explain how to solve them, and talk about how to tell them apart from combination questions. So let's say we have five chairs and we have five people. Let's just call our people person A, person B, person C, person D, and person E. So let's say somebody asks me how many ways can I sit five people in our five chairs? Well, we don't even really need a formula, we just have to think about the possibilities for each chair. So if we look at chair number one, how many people do I have to choose from? Well, I have five. By the time I get to chair number two, I only have four people to choose from. Likewise, when I get to chair number three, I'm down to three choices. Chair number two, I only have two. By the time I get to the final chair, only one person is left. So to figure out how many arrangements that makes, I just multiply all the numbers. So I do five times four is 20 times three, 60 times two is 120, times one, is still 120. So that's a permutation and kind of the key words to look for in a permutation question are ways we can do things and arrangements. And the key thing to remember for this is that order matters. In other words, the arrangement A, B, C, D, E would count differently than the arrangement E, D, C, B, A. Great, so what if we have some kind of restriction to deal with in a permutation? Let's say I had the same five people, the same five chairs, and for some reason, person C won't sit on the end. He or she has a phobia of being on the end chair. So the way that we want to handle this restriction and I'm just going to write restriction down here to differentiate it, we want to kind of place the restriction first. So we're going to think about this person C and we're going to come up with how many possibilities does that person have? Well, they only have three. It's got to be either this chair, this chair, or this chair. That means that the first number in our calculation is going to be a three. Now I know that C won't sit on the end but remember, you can multiply in any order so it doesn't really matter where you write the numbers. Okay, well now that we've dealt with person C, they only have these three possibilities, how many people can be picked from for this next chair. Well, there's four people left, so we'll put a four there. By the time we get to this chair, it's three. This chair, we have two left. And this chair, we have one. So now how many arrangements do we have? We'll just multiply all the numbers again. Three times four is 12, times three, 36 times two, 72. So remember, if you do have a restriction in a permutation, figure out the possibilities for that restriction first, and then calculate the other numbers. So remember, for permutations, order matters. Deal with the restrictions first and make sure that you look for key keywords like ways or arrangements to signify that you're looking at a permutation question.

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