2. Derangements A derangement of (1, 2,..., n is a permutation ii2.in of (1, 2,.., n in which no integer is in its natural position i11,2≠2,…n≠n We denote by d the number of derangements of{1,2,…,n} Theorem4.l5:Forn≥1, D=n!(1 ∴ l!2!13▪ 2.Derangements ▪ A derangement of {1,2,…,n} is a permutation i1 i2…in of {1,2,…,n} in which no integer is in its natural position: ▪ i11,i22,…,inn. ▪ We denote by Dn the number of derangements of {1,2,…,n}. ▪ Theorem 4.15：For n1, ) ! 1 ( 1) 3! 1 2! 1 1! 1 !(1 n D n n n = − + − ++ −