Question

Find the number of one-to-one functions from a set with five elements to sets with 5 elements

Answer 1

If m>n, there aren't any.

If m≤n, there are n options for where to send the first element, n−1 options for the second, n−2 for the third and so on.

So, the total number of 1:1 functions from an m-set to an n-set is

n(n−1)(n−2)⋯(n−m+1)=n/(n−m)