So the things that I left out, the things that I left out, that was essentially the number of people minus the number of chairs, so I was trying to put five I multiplied five times four times three, I kept going until I had that many seats, and then I didn't do the remainder. Where did this two come from? Well, think about it. But then you might have the question where did this two come from? I have three seats. I could write this as five factorial, five factorial, over two factorial, over two factorial. The whole reason I'm writing this way is that now I can write If you did that, this two times one would cancel with that two times one and you'd be left with five So one way to thinkĪbout what we just did, is we just did five times four times three times two times one, but of course we actually didn't do the two times one, so you could take that and you could divide by two times one.

To what we did just now? It looks like we kind of did factorial, but then we stopped. But you might say, hey, when we just did five different people inįive different chairs, and we cared which seat they sit in, we had this five factorial. I like to actually conceptualize and visualize what I'm doing. I just literally draw it out because I don't like formulas. Now this, and my brain, whenever I start to think in terms of permutations, I actually think in these ways. So there's 60 permutations of sitting five people in three chairs. So this is equal to five times four times three scenarios, which is equal to, this is equal to 60. We haven't seaten or sat three of the people yet, so for each of theseĢ0, we could put three different people in seat three, so that gives us five timesįour times three scenarios. For each of those 20 scenarios, how many people could sit in seat three? Well, we haven't sat, So we have five times four scenarios where we've seated seats one and seat two. Who haven't been seated, so four people could sit in seat two. If one person has sat down, there's four people left

Scenarios where one person has already sat in seat one, how many people could sit in seat two? In each of these scenarios, If we seat them in order,Īnd we might as well, how many different people, if we haven't sat anyone yet, how many different peopleĬould sit in seat one? Well, we could have, if no one sat down, we had five different people, five different people I am assuming you have had your go at it. How many ways can you have five people, where only three of themĪre going to sit down in these three chairs, and we care which chair they sit in? I encourage you to pause the We have chair one, we have chair two, and we have chair three. Let's say that we only have three chairs. Have these five people, but we don't have as many chairs, so not everyone is going Maybe more interesting, or maybe you might find Five factorial, which isĮqual to five times four times three times two times one, which, of course, is equal to, let's see, 20 times six, which is equal to 120.

The number of permutations, permutations, of seating these five We only have one person who hasn't sat down left, For each of those, how many possibilities are there for the fifth seat? Well, one. So now there's five times four times three times two scenarios of How many people are left for seat four? Well, two people haven't sat down yet, so there's two possibilities. So now, there's five timesįour times three scenarios for seating the first three people. Now seat in seat three for each of those 20 scenarios? Well, three people haven't sat down yet, so there's three possibilities there. Five times four, we have 20 scenarios where we've seated seat one and seat two, how many people could we Now, for each of these scenarios, now, so we have 20 scenarios. So, for each of those scenarios, four different peopleĬould sit in chair two. If we seated people in order, which we might as well do, we could say, look, five different people could sit in chair one. People in these five chairs, we could say, well, we The number of scenarios, or we could say the number of permutations of putting these five Two, position three, position four, and position five. Them in five different, let's say, positions, or chairs, so position one, position If we had five people, let's say person A, person B, person C, person D, and person E, and we wanted to put

100 permute 3