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Mathematics LibreTexts

21.2: Definition

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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 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.

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