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In a generalized allocation scheme of n particles over N cells we consider the random variable ηn,N(K) which is the number of particles in a given set consisting of K cells. We prove that if n, K, N → ∞, then under some conditions random variables ηn,N(K) are asymptotically normal, and under another conditions ηn,N(K) converge in distribution to a Poisson random variable. For the case when N → ∞ and n is a fixed number, we find conditions under which ηn,N(K) converge in distribution to a binomial random variable with parameters n and s = K N , 0 < K < N, multiplied by a integer coefficient. It is shown that if for a generalized allocation scheme of n particles over N cells with random variables having a power series distribution defined by the function B(β) = ln(1 − β) the conditions n, N, K → ∞, K N → s, N = γ ln(n) + o(ln(n)), where 0 < s < 1, 0 < γ < ∞, are satisfied, then distributions of random variables η n , N (K) n converge to a beta-distribution with parameters sγ and (1 − s)γ. [ABSTRACT FROM AUTHOR]

Let [p.sub.nN] be the probability of successful allocation of n groups of particles in N cells with the following assumptions: (a) each group contains m particles and has allocation as a general allocation scheme; (b) each cell contains at most r particles from the same group; (c) events connected with different groups are independent. We obtain an asymptotically exact bound of [p.sub.nN] as n, N [right arrow] [infinity] such that n/N is bounded. Applications to problems in error-correcting coding are considered., UDC 519.212.2+517.537 1. Introduction and Main Result We will consider a general allocation scheme of n independent series of particles in N cells (for an account of such an allocation [...]