Find the number of all onto functions from the set {1, 2, 3, ..., n} to itself.

Question

Philoid · Accepted Answer

Onto function from the set {1, 2, 3, ..., n} to itself is simply a permutation on n symbols 1, 2, 3, …, n.

Therefore, the total number of onto maps from {1, 2, 3, …, n} to itself is the same as the total number of permutations on n symbols 1, 2, 3, …, n, which is n!