Randomly permute the integers in the set {1, 2, 3, 4, 5}, so that each of the

possible permutations is equally likely to occur. Find

(a) the probability that all of them are in their

natural position, i.e., the permutation turns

out to be exactly {1, 2, 3, 4, 5},

(b) the probability that exactly two of them are in their natural position,

(c) the probability that exactly three of them are in their natural position,

(d) the probability that exactly four of them are in their natural position