Geodesic
Asymptotic behaviour of a~number of groups of particles in a~classical problem of permutation
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 4, pp. 701-708

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Let groups each of $m$ particles be distributed independently into $n$ cells so that particles of every group are distributed into different cells with all ${n\choose m}$ possible permutations having equal probabilities. A random variable $\nu_m(n,t)$ is introduced which is equal to the number of groups whose distribution leads to at least $t$ cells being occupied for the first time. In this paper the whole spectrum of limit theorems is obtained and exact formulae as well as their asymptotic expressions as $n$, $t\to\infty$ of the mean and variance of random variables $\nu_m(n,t)$ are found. 
@article{TVP_1966_11_4_a10,
     author = {G. I. Ivchenko and Yu. I. Medvedev},
     title = {Asymptotic behaviour of a~number of groups of particles in a~classical problem of permutation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {701--708},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {1966},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1966_11_4_a10/}
}
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G. I. Ivchenko; Yu. I. Medvedev. Asymptotic behaviour of a~number of groups of particles in a~classical problem of permutation. Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 4, pp. 701-708. http://geodesic.mathdoc.fr/item/TVP_1966_11_4_a10/