The Subfactorial is Hilarious

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We introduce the subfactorial !n. This counts the number of derangements of a set of n objects, these are the permutations with no fixed points. We introduce the concept with men, their hats, and the wrath of God. We'll use the inclusion exclusion principle to derive an expression for derangements and determine the probability a random permutation is a derangement, finding a surprising friend at the end. #mathematics #maths #combinatorics

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0:00 Intro
1:34 Treacherous Situation
2:18 Derangements
2:51 Permutations
4:30 Finishing Notation
6:35 Begin Argument
12:46 Inclusion-Exclusion
16:26 Count with At Least 1 Fixed Point
19:06 How Likely?
21:30 The Probability
22:07 Final Note