# Difference between revisions of "Derangement"

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A '''derangement''' is a [[permutation]] with no [[fixed point]]s. A derangement can also be thought of as a permutation in which none of the objects are in their original space. For example, the derangements of <math>(1,2,3)</math> are <math>(2, 3, 1)</math> and <math>(3, 1, 2)</math>. The number of derangements of a set of x objects is denoted !x, and is given by the formula: | A '''derangement''' is a [[permutation]] with no [[fixed point]]s. A derangement can also be thought of as a permutation in which none of the objects are in their original space. For example, the derangements of <math>(1,2,3)</math> are <math>(2, 3, 1)</math> and <math>(3, 1, 2)</math>. The number of derangements of a set of x objects is denoted !x, and is given by the formula: | ||

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<math>\displaystyle !x = x! \sum_{k=1}^{n} \frac{-1^k}{k!}</math> | <math>\displaystyle !x = x! \sum_{k=1}^{n} \frac{-1^k}{k!}</math> | ||

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## Revision as of 17:15, 13 November 2006

A **derangement** is a permutation with no fixed points. A derangement can also be thought of as a permutation in which none of the objects are in their original space. For example, the derangements of are and . The number of derangements of a set of x objects is denoted !x, and is given by the formula:

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