[ pur-myoo-tey-shuhn ]
See synonyms for permutation on
  1. the act of permuting or permutating; alteration; transformation.

  2. Mathematics.

    • the act of changing the order of elements arranged in a particular order, as abc into acb, bac, etc., or of arranging a number of elements in groups made up of equal numbers of the elements in different orders, as a and b in ab and ba; a one-to-one transformation of a set with a finite number of elements.

    • any of the resulting arrangements or groups.: Compare combination (def. 8b).

Origin of permutation

1325–75; Middle English permutacioun (<Middle French permutacion) <Latin permūtātiōn- (stem of permūtātiō) thoroughgoing change. See per-, mutation, permute

Other words for permutation

Other words from permutation

  • per·mu·ta·tion·al, adjective
  • per·mu·ta·tion·ist, noun

Words Nearby permutation Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

How to use permutation in a sentence

  • The Manson family was its most grotesque and dangerous permutation.

    My Battle With Manson | Vincent Bugliosi | August 7, 2009 | THE DAILY BEAST
  • The economic reform wrought is largely of the nature of a permutation in the methods of conspicuous waste.

  • We may thus select the four coins in one hundred ways, and the four removed may be arranged by permutation in twenty-four ways.

    Amusements in Mathematics | Henry Ernest Dudeney
  • This permutation is made very convenient by the sentences being printed in sections which may be moved about and combined at will.

  • Nevertheless, it is much easier to give the child a vivid impression of them by the permutation of parts than by explanation.

  • Reputable authority can be quoted in behalf of every possible permutation of doctrine.

British Dictionary definitions for permutation


/ (ˌpɜːmjʊˈteɪʃən) /

  1. maths

    • an ordered arrangement of the numbers, terms, etc, of a set into specified groups: the permutations of a, b, and c, taken two at a time, are ab, ba, ac, ca, bc, cb

    • a group formed in this way. The number of permutations of n objects taken r at a time is n !/(nr)!: Symbol: n P r Compare combination (def. 6)

  2. a combination of items made by reordering

  1. an alteration; transformation

  2. a fixed combination for selections of results on football pools: Usually shortened to: perm

Origin of permutation

C14: from Latin permūtātiō, from permūtāre to change thoroughly; see mutation

Derived forms of permutation

  • permutational, adjective

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012