Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 1 / e / ii / Solution

A bijection between finite sets requires equal cardinality. When $m=n$, list the elements of $A$ and choose their distinct images in $n,n-1,\dots ,1$ ways. ThusThe factorial convention $0!=1$ includes the unique bijection from the empty set to itself.