Suppose we have an alphabet of n letters and we want to count the number of strings of size k over this alphabet where no symbol occurs twice or more....

Suppose we have an alphabet of n letters and we want to count the number of strings of size k over this alphabet where no symbol occurs twice or more. These are thus permutations over a subset of size k of the alphabet . Prove the this number is P(n,k) = n! / (n-k)!