Dear Tutors,

Please help me with the following problem. Thank you in advance!

2)

Question 2 A derangement of {1, 2, . . ., n} is a permutation 172 . . . in of {1, 2, . . . , n} in which no integer is in its natural position: i1 # 1, i2 # 2, . . ., in # n. Let D., be the number of derangements of {1, 2, . .., n} prove the following identity n! = (") Dn + (")Dn-1+ (2) Dn-2 + ... + (,")D1 + (")Do. Here, we define Do to be 1