A derangement of the set {1, 2,…, n} is a permutation that
Chapter 9, Problem 43E(choose chapter or problem)
Problem 43E
A derangement of the set {1, 2,…, n} is a permutation that moves every element of the set away from its “natural” position. Thus 21 is a derangement of {1, 2}, and 231 and 312 are derangements of {1, 2, 3}. For each positive integer n, let dn be the number of derangements of the set {1, 2,…, n}.
a. Find d1, d2, and d3.
b. Find d4.
c. Find a recurrence relation for d1, d2, d3,…
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