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.