permutation
or ordered arrangement, n. 1. an ordered arrangement of a specified number objects selected from a set. The number of distinct permutations of r objects from n is 
usually written nPr or n Pr. For example, there are six distinct permutations of two objects selected out of three: 〈1, 2〉, 〈1, 3〉, 〈2, 1〉, 〈2, 3〉, 〈3, 1〉, 〈3, 2〉. Compare combination.2. any rearrangement of all the elements of a finite sequence, such as (1, 3, 2) and (3, 1, 2). It is odd or even according as the number of exchanges of position yielding it from the original order is odd or even. It is a cyclic permutation if it merely advances all the elements a fixed number of places; that is, if it is a cycle of maximal length. A transposition is a cycle of degree two, and all permutations factor as products of transpositions. See also signature. 3. any bijection of a set to itself, where the set may be finite or infinite.
usually written nPr or n Pr. For example, there are six distinct permutations of two objects selected out of three: 〈1, 2〉, 〈1, 3〉, 〈2, 1〉, 〈2, 3〉, 〈3, 1〉, 〈3, 2〉. Compare combination.2. any rearrangement of all the elements of a finite sequence, such as (1, 3, 2) and (3, 1, 2). It is odd or even according as the number of exchanges of position yielding it from the original order is odd or even. It is a cyclic permutation if it merely advances all the elements a fixed number of places; that is, if it is a cycle of maximal length. A transposition is a cycle of degree two, and all permutations factor as products of transpositions. See also signature. 3. any bijection of a set to itself, where the set may be finite or infinite.