what have you done so far?
suppose there are N different types of coupons and each time one obtains a coupon, it is equally likely to be any one of the N types. Find the expected number of coupons one needs to collect before obtaining a complete set of atleast one of each type
Let X denote the number of coupons collected before a complete set is attained.
Let be the number of additional coupons that need to be obtained after i distinct types have been collected in order to obtain another distinct type.
So,
when you have collected i distinct coupons, you will obtain a new coupon with a probability of
figure out what distribution this is and find its expected value.