permutation

[ pur-myoo-tey-shuhn ]

noun

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

   Synonyms: change, transmutation, modification

2. 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. Compare combination ( def 8b ).

permutation

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

Derived Forms

• ˌpermuˈtational, adjective

Other Words From

• permu·tation·al adjective
• permu·tation·ist noun

Word History and Origins

Origin of permutation¹

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

Word History and Origins

Origin of permutation¹

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

Example Sentences

It’s a hokey setup, but Duchovny is spiritedly determined to work through the various permutations of this man-and-Mammon tale.

From Washington Post

Rejewski applied the branch of mathematics devoted to permutations to the problem — an approach that would look obvious only after he used it.

From Washington Post

That a story set in 19th-century England thrives in this country so ubiquitously, in so many permutations, remains a bit of a wonder.

From Washington Post

This problem was equivalent to finding the probability that a random permutation of five people was also a derangement, meaning no one wound up in their own starting position.

From FiveThirtyEight

Usually in order to find them you need to go fishing in the sea of permutations of different elements.

From Quanta Magazine

The Manson family was its most grotesque and dangerous permutation.

From The Daily Beast

The economic reform wrought is largely of the nature of a permutation in the methods of conspicuous waste.

From Project Gutenberg

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

From Project Gutenberg

This permutation is made very convenient by the sentences being printed in sections which may be moved about and combined at will.

From Project Gutenberg

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

From Project Gutenberg

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

From Project Gutenberg