A rearrangement
of a number of objects is called a permutation.

Suppose Ann, Bob
and Carole are to sit on three chairs side by side. Then there are
6 different orders in which they could be placed on the chairs,
each being a permutation of the 3 people.

ABC BCA CAB BAC CBA ACB.

There are two main notations for such permutations. In relation
notation, one can just arrange the natural ordering of the
elements being permuted on a row, and the new ordering on
another row.

The general case is given by the formula :

where, n is the number of elements available for selection, and

r is the number of elements to be selected.