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We consider a two-stage scheme of allocating particles into cells. At the first stage,  N  0  initial particles are independently and equiprobably allocated into  N  1  cells of the first layer. At the second stage, these  N  1  cells are taken as particles which are independently and equiprobably allocated into  N  2  cells of the second layer. We present conditions under which the distribution of the number of cells of the second layer containing exactly  r  particles converges to the Poisson law.

A Poisson limit theorem for a two-stage equiprobable scheme of allocating particles into cells