12. Coupon-collecting problem. There are c different types of coupon, and each coupon obtained is equally likely to be any one of the c types. Let Yi be the additional number of coupons collected, after obtaining i distinct types, before a new type is collected. Show that Yi has the geometric distribution with parameter (c −i )/c, and deduce the mean number of coupons you will need to collect before you have a complete set.