Limit theorems for the number of empty cells in the equiprobable scheme of group disposal of particles

Let $n$ groups of particles ($i^{th}$ group contains $s_i$ particles) are placed independently into $N$ cells so that each cell contains at most one particle of each group and all $C_N^{s_i}$ possible dispositions of particles of $i^{th}$ group are equiprobable. In this paper Poisson and normal limit theorems for the number of empty cells are obtained. In all cases the estimates of the rate of convergence to the limit distributions are given. These results complete and generalize some known theorems (see [1]–[7]).