Sitting in three chairs, how many ways can I choose This is all the same set of three people if we don't care whichĬhair they're sitting in.

So in that world, these would all be one.

But what if we, what if all we cared about is the three people we're choosing to sit down, but we don't care in what order that they're sitting, or in which chair they're sitting. So in the permutation world, these are, these are literally 12 I'm going to be a littleīit more systematic. Where we have, it couldīe F, B, C, F, C, B, F, A, C, F, F. And of course we have other permutations where we would involve other people. So our thinking in the permutation world. We could have that, or we could have that. The same three people, but we're putting them This would be countedĪs another permutation. And this would be countedĪs another permutation. When we're talking about permutations, we care about who's sitting in which chair. Now it's worth thinking about what permutations are counting. So your total number of scenarios, or your total number of permutations where we care who's sitting in which chair is six times five times four, which is equal to 120 permutations. So for each of these 30 scenarios, you have four people who you could put in chair number three. To have four people standing up not in chairs. And now if you want to say well what about for the three chairs? Well for each of these 30 scenarios, how many different people could you put in chair number three? Well you're still going So you have a total of 30 scenarios where you have seated six You have five scenarios for who's in chair number two. Someone in chair number one and for each of those six, Or another way to think about it is there's six scenarios of So that means you haveįive out of the six people left to sit in chair number two. Scenarios we've taken one of the six people to Now for each of those six scenarios, how many people, how many different people could sit in chair number two? Well each of those six There are six people whoĬould be in chair number one. We put in chair number one? Well there's six different And we can say look if no one's sat- If we haven't seated anyone yet, how many different people could Permutations of putting six different people into three chairs? Well, like we've seen before, we can start with the first chair. But it'll be very instructive as we move into a new concept. This is covered in the permutations video. One, chair number two and chair number three. Out all the scenarios, all the possibilities,Īll the permutations, all the ways that we could Video, we're going to say oh we want to figure Person B, we have person C, person D, person E, and we have person F. About different ways to sit multiple people in

Does order matter in permutations