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This paper gives an algebraic proof of the correctness of Von Schellingformula for the probability of the coupon collector problem waiting time fornon-uniform distributions and partial collections. It introduces a theorem onsums of powers of subset probabilities which to our knowledge is new. A set ofbinomial coefficients is used as a basis for decomposition of these sums ofpowers.

On Von Schelling Formula for the Generalized Coupon Collector Problem