Number of Permutations of All Elements/Proof 3

Proof
From the definition, it can be seen that a bijection $f: S \to S$ is an $n$-permutation.

Hence, from Cardinality of Set of Bijections the number of $n$-permutations on a set of $n$ elements is:
 * ${}^n P_n = \dfrac {n!} {\paren {n - n}!} = n!$