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One of the different orders in which you can place a given set of things.
If you had two words - 'cat' and 'sat', then the only phrases you could write are: 'cat sat' or 'sat cat'.
If you had three words - cat, sat and mat then the phrases you could write are:
'cat sat mat'
'cat mat sat'
'sat mat cat'
'sat cat mat'
'mat cat sat'
'mat sat cat'
Two words had two permutations, while three words had six rearrangements.

An order of arranging a given set of objects.

An ordered arrangement of a specified number of objects from a set; this can also be considered a mapping from a finite or countable set onto itself. The number of distinct permutations of r objects from n is

nPr = n! (n−r)! .

Any rearrangement of all the elements of a finite sequence. It is odd or even depending on whether the number of exchanges of position yielding it from the original position 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 fixed length. A transposition is a cycle of degree two, and all permutations factor as products of transpositions. Note that the set of all permutations of a set of size n form a group, often written S_n , under composition; there is a subgroup A_n of all even permutations. See also signature. Any bijection of a set to itself, where the may be finite or infinite.