Finite permutation group/Cardinality/Fact
< Finite permutation group < Cardinality
Let
M
{\displaystyle {}M}
be a finite set with
n
{\displaystyle {}n}
elements.
Then the
permutation group
Perm
(
M
)
≅
S
n
{\displaystyle {}\operatorname {Perm} \,(M)\cong S_{n}\,}
contains exactly
n
!
{\displaystyle {}n!}
elements.
Proof
,
Write another proof
be a finite set with 
elements. 
