Inclusion/Exclusion

The Inclusion/Exclusion Principle is a formula that allows us to compute the cardinality of a finite union, or intersection, of finite sets. We present the most popular applications of the Principle, like finding the number of surjective applications between two finite sets, or the number of derangements, i.e., point free permutations, of (1, …, n) : this leads us to show that, collecting at random a hat at the wardrobe, the probability that nobody recovers their own hat tends to 1 / e as the number of people grows. The curious reader will find some more special results, like the computation of the number of derangements of a sequence with repetitions.