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On a classical problem of probability theory. (English) Zbl 0102.35201
The authors consider the following problem: The balls are placed at random into \(n\) urns numbered by \(1,2,...,n\). Each ball may be placed in any of the urns with the same probability and the choices of the urns for the different balls are independent. The process of placing balls in the urns is continued till there are at least \(m\) balls in every urn. The number of balls which are needed to achieve this goal is denoted by \(\nu_m (n)\). The authors give the asymptotic probability distribution of \(\nu_m (n)\).
Reviewer: L.Kubik

60C05 Combinatorial probability