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

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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.

$\blacksquare$


Sources