Cardinality of Set of Bijections
Let $S$ and $T$ be sets such that $\size S = \size T = n$.
Then there are $n!$ bijections from $S$ to $T$.
Follows directly from Cardinality of Set of Injections and Equivalence of Mappings between Sets of Same Cardinality.
- $\card S = 4$
Then there are $24$ bijections from $S$ to itself.