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A classical scheme of random equiprobable allocations of  n  particles into  N  cells is considered. We find an asymptotic formula for the probability that the number of empty cells is equal to  k  under the condition that  n ,  N  → ∞ in such a way that  n /( N  −  k ) is bounded and separated from 1 from below.

Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations