Permutation

A permutation of a set of r objects is any rearrangement of the r objects. There are (the factorial of r) permutations of a set with r objects.

An important question is how many ways to pick an r-element subset of a set with n elements, where order matters. To find how many ways we can do this, note that for the first of the r elements, we have n different objects we can choose from. For the second element, there are (n-1) objects we can choose, (n-2) for the third, and so on. In general, the number of ways to permute r objects from a set of n is given by .