Coupons collecting with or without replacement, and with multipurpose   coupons
  The classic Coupon-Collector Problem (CCP) is generalized to the extent that each coupons serves certain "purposes". Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all $k$-element transversals of a set system. 
Marcel Wild, Svante Janson, Stephan Wagner and Dirk Laurie
math.PR cs.DM