In
abstract algebra, the
symmetric group S
n on a
finite set of
n symbols is the
group whose elements are all the
permutation operations that can be performed on
n distinct symbols, and whose
group operation is the
composition of such permutation operations, which are defined as
bijective functions from the set of symbols to itself. Since there are
n! (
n factorial) possible permutation operations that can be performed on a
tuple composed of
n symbols, it follows that the
order (the number of elements) of the symmetric group S
n is
n!.