Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 3 / a / i / Solution

A derangement of a finite set $A$ is a permutation $\sigma :A\to A$ with no fixed point: $\sigma (a)\ne a$ for every $a\in A$. Thus every element is moved, although the permutation remains a bijection.