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We study the random variable  B ( c, n ), which counts the number of balls that must be thrown into  n  equally‐sized bins in order to obtain  c  collisions. The asymptotic expected value of  B (1,  n ) is the well‐knownn  π  /  2appearing in the solution to the birthday problem; the limit distribution and asymptotic moments of  B (1,  n ) are also well known. We calculate the distribution and moments of  B ( c, n ) asymptotically as  n  goes to  ∞  and  c  =  O ( n ). We have two main tools: an embedding of the collision process — realizing the process as a deterministic function of the standard Poisson process — and a central limit result by Rényi. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 480–502, 2016

Asymptotic distribution for the birthday problem with multiple coincidences, via an embedding of the collision process