Cardinality of Set of Bijections

Theorem
Let $S$ and $T$ be finite sets with the same cardinality:
 * $\size S = \size T = n$

Then there are $n!$ bijections from $S$ to $T$.

Proof
Follows directly from Cardinality of Set of Injections and Equivalence of Mappings between Finite Sets of Same Cardinality.