There are N people in a room, each wearing a different hat. They all take their hats off, put them together and then each randomly picks one up. What is the probability of no person getting their own hat back (denote this event by A)? What does this probability become as N → ∞ ? Can somebody give me some ideas, please?
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What have you tried? What techniques are available to you? Probably the most systematic and universal approach is the method of inclusion-exclusion. – LetGBeTheGraph Oct 20 '20 at 15:07
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You can refer to this post: https://math.stackexchange.com/questions/1589915/problem-with-people-and-hats-after-lunch?rq=1 – 0Interest Oct 20 '20 at 15:07
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2See this. – cosmo5 Oct 20 '20 at 15:07
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5Does this answer your question? Problem with people and hats after lunch – cosmo5 Oct 20 '20 at 15:11
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1The word to google: derangement. – CiaPan Oct 20 '20 at 16:15