In this article we study a number of collisions concerning a simple occupancy problem with unequal probabilities. Using combinatorial arguments and negative associations of random variables, we have several limit theorems, namely, a weak law of large numbers and a Poisson law of small numbers including the Chen-Stein estimate.
"The number of collisions for the occupancy problem with unequal probabilities." Adv. in Appl. Probab. 46 (1) 168 - 185, March 2014. https://doi.org/10.1239/aap/1396360108