# Permutations - Problem 1

So an application of permutations is typically when we are sort of categorizing an event and what we're going to look at now is runners in a race.

So we have 7 runners and what we are looking at is the different ways that they can medal, different ways they could place. And so one way we can do is just by writing out all the different options. We have to have one person to be gold and there are 7 people, so you have 7 people that could be gold, once that person wins one gold, there are now 6 that could get silver and then there is 5 that could get bronze, so what we're going to end up with is 7 times 6 times 5.

But the other way we can do this is doing permutations and basically what that means is just the number of total things we're looking at in this case 7 and then permute the number of things that we are interested. There is 3 people that medal so basically 7 permute 3.

If we were to distribute this out, what we would end up with is 7 times 6 times 5 so for this particular example it would be easy enough to write out our options, but to get used to how the permutation idea works, let's just jump into 7 permute 3, they're both the same thing.

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