Counting Derangements in Combinatorics

Derangements in combinatorics are permutations with no fixed points, meaning no element gets mapped to itself. In this video, we use the principle of inclusion-exclusion (PIE) to derive as simple as possible a formula for the number of derangements of a given finite set. Amazingly, it turns out that, as the number of elements goes to infinity, the fraction of permutations that are derangements approaches the reciprocal of Euler's constant e. Wow!

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[ugandamathcontest]

Thanks for the great explanation. It has helped in my preparation for IMO, Ugandan team