Permutations

We now move from simply counting arrangements to a precise way of describing them. A permutation is any ordered arrangement of a set of objects — changing the order gives a different permutation. The key idea is that order matters, which is why the number of permutations of $n$ distinct objects taken $r$ at a time is given by $^nP_r = \frac{n!}{(n-r)!}$. This formula will be our main tool for solving problems …