Number of k-Cycles in Symmetric Group

Theorem
Let $n \in \N$ be a natural number.

Let $S_n$ denote the symmetric group on $n$ letters.

Let $k \in N$ such that $k \le n$.

The number of elements $m$ of $S_n$ which are $k$-cycles is given by:
 * $m = \paren {k - 1}! \dbinom n k = \dfrac {n!} {k \paren {n - k}!}$