A Berry-Esseen bound is given for the rate of convergence to normality of the number of empty boxes when balls are distributed independently and at random to boxes with possibly unequal probabilities. The method of proof uses the equivalence of this distribution to a certain conditional distribution based on independent Poisson random variables. Then methods based on the characteristic function of this conditional distribution are used to obtain the result.
"A Berry-Esseen Bound for an Occupancy Problem." Ann. Probab. 10 (3) 663 - 671, August, 1982. https://doi.org/10.1214/aop/1176993775