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The "double Dixie cup problem" of D.J. Newman and L. Shepp (1960) is awell-known variant of the coupon collector's problem, where the object of studyis the number $T_{m}(N)$ of coupons that a collector has to buy in order tocomplete $m$ sets of all $N$ existing different coupons. More precisely, theproblem is to determine the asymptotics of the expectation (and the variance)of $T_{m}(N)$, as well as its limit distribution, as the number $N$ ofdifferent coupons becomes arbitrarily large. The classical case of the problem,namely the case of equal coupon probabilities, is here extended to the generalcase, where the probabilities of the selected coupons are unequal.  In the beginning of the article we give a brief review of the formulas forthe moments and the moment generating function of the random variable$T_{m}(N)$. Then, we develop techniques of computing the asymptotics of thefirst and the second moment of $T_{m}(N)$ (our techniques apply to the highermoments of $T_{m}(N)$ as well). From these asymptotic formulas we obtain theleading behavior of the variance $V[\,T_{m}(N)\,]$ as $N \to \infty$. Finally,based on the asymptotics of $E[\,T_{m}(N)\,]$ and $V[\,T_{m}(N)\,]$ we obtainthe limit distribution of the random variable $T_{m}(N)$ for large classes ofcoupon probabilities. As it turns out, in many cases, albeit not always,$T_{m}(N)$ (appropriately normalized) converges in distribution to a Gumbelrandom variable. Our results on the limit distribution of $T_{m}(N)$ generalizea well-known result of P. Erd\H{o}s and A. R\'{e}nyi (1961) regarding the limitdistribution of $T_{m}(N)$ for the case of equal coupon probabilities.

The Coupon Collector's Problem Revisited: Generalizing the Double Dixie Cup Problem of Newman and Shepp