In case you're wondering a derangement is a permutation that has no fixed points. Exact formula !n=n! ∑ᵢ₌₀ⁿ(-1)ⁱ/i!
Recursive formula !n=[n-1][!(n-1)+!(n-2)] with !1=0 and !2=1,
And of course, good old @numberphile & @jamesgrime have got you covered!https://youtu.be/pbXg5EI5t4c
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The nth subfactorial is the number of permutations of n objects in which no object appears in its natural place. Long story short: it's alternating series of permutations.pic.twitter.com/2iWzvZJrsw
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[inspired from wikipedia] Suppose that a professor gave a test to 4 students – A, B, C, and D – and wants to let them grade each other's tests, but no student should grade his/her own test. Out of 24 possible permutations (4!), there are only 9 derangements (blue italics in fig)pic.twitter.com/P9uwitkq0B
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!n ≈ n! / e
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Thanks...tested it and it is correct
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Apparently !0=1 but this confuses me
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None, because of the Patronus Charm.
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