I have been trying to find the proof of the derangement theorem, and have checked out some materials on them (since its proof has not been taught to us). But I have not been able to understand much of it. So, I was thinking, is the inclusion-exclusion principle used? Since the expression seems somewhat familiar. If not, then could someone please explain the proof in a slightly simplified manner?
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Dernagements – lulu Sep 05 '23 at 15:09
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I am not aware of a "derangement theorem" but I am well familiar with derangements. If the linked post does not provide enough detail, specify what is still missing. – JMoravitz Sep 05 '23 at 15:12
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@JMoravitz I have checked the attached post, and it is well above my level. What I meant by the derangement theorem was just the formula "DN= N![1-1/1!+1/2!-1/3!…1/N!]", I should have specified that, sorry. – Anne Sep 05 '23 at 16:02
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@lulu Thank you, guess I forgot to check out the most obvious source, sorry! – Anne Sep 05 '23 at 16:02
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I have read the article, and checked the principle of inclusion-exclusion proof in the answer also. However, I just wanted to clarify that we can see this from the venn diagram perspective, right? As in we draw venn diagram of 5 objects being put in their designated boxes, compute the sum of the ways using set theory, and then subtract this from the total number of ways of putting the objects into the boxes. – Anne Sep 05 '23 at 16:06