In
mathematics, the notion of
permutation relates to the act of
arranging all the members of a
set into some
sequence or
order, or if the set is already ordered,
rearranging (reordering) its elements, a process called
permuting. These differ from
combinations, which are selections of some members of a set where order is disregarded. For example, written as
tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). These are all the possible orderings of this three element set. As another example, an
anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters. The study of permutations of
finite sets is a topic in the field of
combinatorics.
