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This paper gives an algebraic proof of the correctness of Von Schelling formula for the probability of the coupon collector problem waiting time for non-uniform distributions and partial collections. It introduces a theorem on sums of powers of subset probabilities which to our knowledge is new. A set of binomial coefficients is used as a basis for decomposition of these sums of powers.
[1] Bruno Sericola,et al. New results on a generalized coupon collector problem using Markov chains , 2015 .
[2] H. V. Schelling. Coupon Collecting for Unequal Probabilities , 1954 .