We're saying if we start with 120 people, and we want to choose. Putting them into three chairs? That's 120. If you said how many differentĪrrangements are there of taking six people and To 120 divided by six, or this would be equal to 20. You can arrange it in six different ways. And we see that you canĪrrange three people, or even three letters.

Number of ways to arrange,Īrrange three people. It by the number of ways to arrange three people. Ways are there to choose three from the six? You would take your whole permutations. And so if all you want to do is care about well how many different Group of three people, that turned into six permutations. Where we've picked a group of three people.

Well a big clue was when we essentially wrote all of the permutations Which chair they sit on? And I encourage you to pause the video, and try to think of what that Three people out of the six where I don't care 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. In other words it is now like the pool balls question, but with slightly changed numbers.About different ways to sit multiple people in This is like saying 'we have r + (n−1) pool balls and want to choose r of them'. So (being general here) there are r + (n−1) positions, and we want to choose r of them to have circles. Notice that there are always 3 circles (3 scoops of ice cream) and 4 arrows (we need to move 4 times to go from the 1st to 5th container). So instead of worrying about different flavors, we have a simpler question: 'how many different ways can we arrange arrows and circles?' Let's use letters for the flavors: (one of banana, two of vanilla): Let us say there are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla.

When to use combination vs permutation