Category:Number of Derangements on Finite Set
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This category contains pages concerning Number of Derangements on Finite Set:
Closed Form for Number of Derangements on Finite Set
The number of derangements $D_n$ on a finite set $S$ of cardinality $n$ is:
| \(\ds D_n\) | \(=\) | \(\ds n! \paren {1 - \dfrac 1 {1!} + \dfrac 1 {2!} - \dfrac 1 {3!} + \cdots + \dfrac {\paren {-1}^n} {n!} }\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds !n\) | where $!n$ denotes the subfactorial of $n$ |
Recurrence Relation for Number of Derangements on Finite Set
The number of derangements $D_n$ on a finite set $S$ of cardinality $n$ is:
- $D_n = \paren {n - 1} \paren {D_{n - 1} + D_{n - 2} }$
where $D_1 = 0$, $D_2 = 1$.
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Pages in category "Number of Derangements on Finite Set"
The following 6 pages are in this category, out of 6 total.