21.2: Definition

Elementary Foundations: An Introduction to Topics in Discrete Mathematics · LibreTexts

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    We often want to count how many ways we can “mix up” the objects in a collection.

    Definition: Permutation

    a bijection from a finite set to itself

    Remark \(\PageIndex{1}\)

    Once you have written the elements of a finite set in some order, think of a permutation as a way of re-ordering them.

    Example \(\PageIndex{1}\): Permutations of three objects.

    Figure \(\PageIndex{1}\) contains tables of values for all six possible permutations of the set \(A = \{a,b,c\}\text{.}\) We have grouped them according to: all elements fixed; one element fixed and two mixed; all elements mixed.

    clipboard_e9c0254032aea9a86f2b29642d7cf5a20.png
    Figure \(\PageIndex{1}\): All possible permutations on three objects.

    This page titled 21.2: Definition was last modified on Tue, 01 Sep 2026 03:35:32 GMT and is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Jeremy Sylvestre via source content that was edited to the style and standards of the LibreTexts platform.