[math-fun] The importance of being a coupon-collector

Mama don't allow no p*l*t*c*l probability here: so I've gone back to collecting --- computationally rather expensive --- coupons. [ A man should have an occupation of some sort. ] I don't know in advance how many distinct coupons are available, but have collected m among which there are just k distinct. What is the probability that n distinct coupons are available? What is the most likely value of n ? What are asymptotic expressions for large m ? Fred Lunnon