Consider N urns into which n balls are dropped independently with equal probability of hitting each urn and constant probability p of staying in the urn. This paper finds the characteristic function of the joint distribution of KN and LN where KN is the number of urns that have not been hit, and LN is the number of urns where all balls have fallen through. Furthermore, it studies the asymptotic distribution of (KN,LN) as n,N⇒• at various rates.
