Suppose $n$ balls are placed into $N$ cells with arbitrary probabilities. Limit distributions for the number of empty cells are considered when $N \rightarrow \infty$ and $n \rightarrow \infty$ in such a way that $n/N \rightarrow \infty$. Limit distributions for the number of balls to achieve exactly $b$ empty cells are obtained for $N \rightarrow \infty$ with $b$ fixed and for $b \rightarrow \infty$ with $b/N \rightarrow 0$.
"Some Asymptotic Results for Occupancy Problems." Ann. Probab. 5 (6) 1028 - 1035, December, 1977. https://doi.org/10.1214/aop/1176995671