The Subfactorial is Hilarious

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Join the channel to get exclusive and early videos, original music, lecture videos, and more! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out the coolest math clothes in the world: https://mathshion.com/ More Math Chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO 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 Textbooks I Like! Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/4d5HbUQ Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 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