Suppose there are n types of coupons, and that the type of each new coupon obtained is independent of past selections and is equally likely to be any of the n types. Suppose one continues collecting until a complete set of at least one of each type is obtained. (a) Find the probability that there is exactly one type i coupon in the final collection. Hint: Condition on T, the number of types that are collected before the first type i appears. (b) Find the expected number of types that appear exactly once in the final collection.