There are $B$ urns. There are $n$ red balls and $n$ white balls with $n\leq B$. Each ball is independently put into each urn with equal probability. An urn can get at most one ball with the same color but can get two balls of different colors. I want to know the probability distribution of the number of urns which contain the balls with different color.
Is there any existing distribution describing this? If not, do you have your own answer?