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What would you guess derangement means in mathematics?
No, we are not describing mathematicians or what they do, but the same people who gave us irrational numbers, gave us deranged permutations. Imagine 5 people each wearing a different hat. They toss the hats in a box and randomly select one. What do you think it would mean for the final hat distribution to be a derangement of the original? It does make sense in an odd sort of way.
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