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.

---

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

---

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

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

Many of these “heritage Americans,” along with every other permutation of U.S. citizens, decided to fight back on behalf of their immigrant friends, neighbors and co-workers.

From Salon • Dec. 27, 2025

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

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