permutation
An ordering of a certain number of elements of a
given set.
For instance, the permutations of (1,2,3) are (1,2,3) (2,3,1)
(3,1,2) (3,2,1) (1,3,2) (2,1,3).
Permutations form one of the canonical examples of a "{group}"
- they can be composed and that you can find an inverse
permutation that reverses the action of any given permutation.
A permutation is a {bijection}.
The number of permutations of r things taken from a set of n
is
n P r ◦ n! / (n-r)!
where "n P r" is usually written with n and r as subscripts
and n! is the {factorial} of n.
What the football pools call a "permutation" is not a
permutation but a {combination} - the order does not matter.
(1995-04-10)