1. 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 you can find an inverse permutation that reverses the action of any given permutation.

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.

2. A bijection for which the domain and range are the same set and so

f(f'(x)) = f'(f(x)) = x.