Harry, Ron and Neville are having a race on their broomsticks.  If there are no ties, in how many different possible orders can they finish?
I need to count the number of permutations of three people, since the order matters. I recall that the formula for the number of permutations of n objects is n!, which means n times (n-1) times (n-2) and so on down to 1. In this case, n = 3, so the number of permutations is 3!, which is 3 times 2 times 1, which is 6. Therefore, there are 6 different possible orders in which Harry, Ron and Neville can finish the race. 