permutation

American  

[pur-myoo-tey-shuhn] / ˌpɜr myʊˈteɪ ʃən /

noun

1. the act of permuting or permutating; alteration; transformation.

   Synonyms:

   change, transmutation, modification

2. an arrangement of a set of objects or elements in a specific order or placement.

3. Mathematics.

   1. 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.

   2. any of the resulting arrangements or groups.

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permutation British  

/ ˌpɜːmjʊˈteɪʃən /

noun

1. maths

   1. 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

   2.  nPr.  a group formed in this way. The number of permutations of n objects taken r at a time is n !/( n – r )! Compare combination

2. a combination of items made by reordering

3. an alteration; transformation

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

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Other Word Forms

• permutational adjective
• permutationist noun

Etymology

Origin of permutation

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

Explanation

A permutation is a change or variation, like the many possible permutations of hair color you get when you start experimenting with different dyes. Permutation is made of the prefix per for "thoroughly" and mutation, which means “change.” A permutation is a thorough change of something, like a substitution. Asking a waiter to give you sweet potato fries instead of regular fries is a permutation. Switching hats with a friend is a permutation. If you switch hats with five of your friends, you'll have many fashion permutations to choose from. Permutations are also like replacements or switches.

Example Sentences

History is littered with examples of big media mergers going awry, many of them involving some permutation of Warner Bros.:

From MarketWatch • Feb. 27, 2026

“But it’s just another permutation of what you take home when you go to the movies.”

From The Wall Street Journal • Feb. 13, 2026

It is a similar permutation for second-placed Doncaster Rovers, who host Colchester, a team who sit level on points with Grimsby in the final play-off spot.

From BBC • Apr. 20, 2025

Directors can arrange a proscenium stage, an open black box space or a theater in the round — along with every possible permutation in between.

From Los Angeles Times • Dec. 26, 2023

White men dominated the crowd from front to back, the majority in some permutation of shirtsleeves and ties or jackets and sweaters, a good number in the coveralls of mechanics and laborers.

From "Hidden Figures" by Margot Lee Shetterly