Permutation is the rearrangement of objects or symbols into distinguishable sequences. Each unique ordering is called a permutation. For example, with the numerals one to six, each possible ordering consists of a complete list of the numerals, without repetitions. There are 720 total permutations of these numerals, one of which is: "4, 5, 6, 1, 2, 3".

The general concept of permutation can be defined more formally in different contexts:

* In set theory, a permutation is an ordered sequence containing each symbol from a set once, and only once. A permutation is distinct from a set or combination, in that the ordering of elements in a set is not considered relevant for sets or combinations. In other words, the set-theoretic definition of permutation is that of a one-to-one correspondence, or bijection, of labeled elements with "positions" or "places" which are arranged in a straight line.
* In abstract algebra and related areas, the elements of permutation may not be arranged in a linear order, or indeed in any order at all. Under this refined definition, a permutation is a bijection from a finite set, X, onto itself. This allows for the definition of groups of permutations; see permutation group.
* In combinatorics, the term permutation also has a traditional meaning which includes ordered lists without repetition and where one or more elements from the list are omitted from the distinguishable orderings; for example, a permutation of "1,2,4,3" with "5" and "6" omitted.