permutation

UK: /ˌpɜː^rmjʊˈteɪʃ^ən/

US: /ˌpɝmjʊˈteɪʃən/

US: (pûr′myŏŏ tā′shən)

WordReference Random House Learner's Dictionary of American English © 2026

per•mu•ta•tion /ˌpɜrmyʊˈteɪʃən/   n. 

1. [uncountable] the act of permuting;
   rearrangement.
2. Mathematics any of the changes that result from such rearrangement:
   [countable] Two of the possible permutations of the elements abc are acb or bac.

See -mut-.

WordReference Random House Unabridged Dictionary of American English © 2026

per•mu•ta•tion  (pûr′myŏŏ tā′shən), n. 

1. the act of permuting or permutating;
   alteration;
   transformation.
2. Mathematics
   • 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. Cf. combination (def. 8b).

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

per′mu•ta′tion•al, adj. 
per′mu•ta′tion•ist, n. 
Synonyms

• 1. modification, transmutation, change.

Collins Concise English Dictionary © HarperCollins Publishers::

permutation / ˌpɜːmjʊˈteɪʃən/ noun

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. a group formed in this way. The number of permutations of n objects taken r at a time is n!/(n–r)!
   Symbol: _nP_r
   Compare combination6
3. a combination of items made by reordering
4. an alteration; transformation
5. a fixed combination for selections of results on football pools
   Usually shortened to: perm

Etymology: 14th Century: from Latin permūtātiō, from permūtāre to change thoroughly; see mutation

ˌpermuˈtational adjective