This lesson describes how to calculate the number of distinct permutations when selecting r things from n choices. (The number of distinct permutations is different than the number of (regular) permutations when the set of n has repeats. For example, how many ways can you rearrange the letters in MOM? The answer is 3 even though perm(3,3) = 6.) This is my own formula/algorithm that I developed while teaching precalculus. Our textbook described how to find the number of distinct permutations when choosing n things from n choices, and it described how to find the number of (normal) permutations when choosing r things out of n distinct choices, but it didn't combine them; it didn't say what do do when you want a subset AND there are repeats in the set of n.

*Note: The involved math and notation can be a little daunting. I think it helps to start at the end and work backwards.