Background About Permutations and Probability

For our purposes, a permutation can be thought of as a one-to-one mapping of the set of
integers
onto itself. The group of all permutations of *n* numbers is
known as the symmetric group, *S*_{n}, and it is a simple matter to verify that there are *n*!permutations in *S*_{n}. In standard notation, a permutation
is written as

where is the image of 1 under , is the image of 2, and so on.