There are n distinct types of coupons, and each coupon obtained is, independently of prior...

There are n distinct types of coupons, and each coupon obtained is, independently of prior types collected, of type iwith probability .

(a) If ncoupons are collected, what is the probability that one of each type is obtained?

(b) Now suppose that p1 = p2= ... = pn = 1/n. Let Ei, be the event that there are no type icoupons among the n collected. Apply the inclusion-exclusion identity for the probability of the union of events to P(∪iEi) to prove the identity