Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Derangement

Revision as of 17:14, 13 November 2006 by Mysmartmouth (talk | contribs)

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 $(1,2,3)$ are $(2, 3, 1)$ and $(3, 1, 2)$. The number of derangements of a set of x objects is denoted !x, and is given by the formula:

$\displaystyle !x = x! \sum_{k=1}^{n} \frac{-1^k}{k!}$

This article is a stub. Help us out by expanding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Derangement&oldid=11724"