Cardinality of Set of Bijections/Examples/Set of Cardinality 4

Examples of Use of Cardinality of Set of Bijections
Let $S$ be a set whose cardinality is $4$:


 * $\card S = 4$

Then there are $24$ bijections from $S$ to itself.

Proof
Let $T$ be the set of bijections from $S$ to itself.

From Cardinality of Set of Bijections:
 * $\card T = \paren {\card S}!$

The result follows by Examples of Factorials.