A derangement is a permutation in which no element appears in its original position. Give a...

 

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A derangement is a permutation in which no element appears in its original position. Give a combi- natorial proof that: n! = =(") do + (") d₁ + (2) dz + ... + (") da, where d, is the number of derangements of n objects. A derangement is a permutation in which no element appears in its original position. Give a combi- natorial proof that: n! = =(") do + (") d₁ + (2) dz + ... + (") da, where d, is the number of derangements of n objects.

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Concept The proof hinges on the idea of constructing all possible arrangements of n objects We can categorize these arrangements based on the number o... View the full answer