Order of Symmetric Group

Theorem
Let $S$ be a finite set of cardinality $n$

Let $\struct {\Gamma \paren S, \circ}$ be the symmetric group on $S$.

Then $\struct {\Gamma \paren S, \circ}$ has $n!$ elements (see factorial).

Proof
A direct application of Cardinality of Set of Bijections.