Number of permutations

Builds on Cardinality of a finite set Factorial Permutation

Statement

Let $X$ be a finite set with $|X| = n$ . Then the number of permutations of $X$ is $n!$ .

Remarks

For $n = 3$ there are $3! = 6$ permutations of $\{1, 2, 3\}$ : $123$ , $132$ , $213$ , $231$ , $312$ and $321$ . The count follows from the rule of product. The image of the first element has $n$ choices, the image of the second has $n - 1$ choices, and so on. It is the case $k = n$ of the number of injections.

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Cardinality of a finite set definition
Factorial definition
Permutation definition
Number of permutations statement

Tag	`0CEBCS0E0E`
URI	`m2://0CEBCS0E0E`
Kind	statement, theorem
Writing	W0 stub
MSC	05A05
Status	This copy of the site has no build data. Run `m2 status 0CEBCS0E0E`.
Uses	Cardinality of a finite set, Factorial, Permutation

Number of permutations

Statement

Remarks

Reading path

Further reading

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