Let n be a positive integer. Suppose we choose a sequence i1, . . . , in of integers, where each number is chosen independent and uniformly at random from the numbers {1, 2, . . . , n}. In other words, the sequence i1, . . . , in consists of n numbers chosen uniformly at random with replacement from {1, 2, . . . , n}. (a) What is the probability that the sequence contains exactly n 2 different integers? (b) What is the probability that the sequence contains exactly n 3 different integers?