# Throw 3 balls into 3 bins find range, distribution, and partition based on following information

There are 3 indistinguishable balls and 3 distinguishable bins.

Let random variable X = #balls in bin 1 and random variable N = #occupied bins

Range(X) = {0,1,2,3} Range(N) = {1,2,3}

A0 = No balls in bin 1, A1 = 1 ball in bin 1, A2 = 2 balls in bin 1, A3 = 3 balls in bin 1,

B1 = 1 occupied bin, B2 = 2 occupied bins, B3 = 3 occupied bins,

How do I find the distribution of each case and eventually the joint distribution?

• What do you mean by "finding the partition"? Apr 5, 2014 at 22:46
• I got confused with some of the definitions. The partition of X would be {A0, A1, A2, A3, A4, A5} and N would be {B1, B2, B3}. Apr 5, 2014 at 22:55

For these numbers I'd be tempted to simply temporarily consider the three balls distinguishable, write down all 27 combinations of which balls go in which bins, and count the number of possible combinations for each of the 12 $(X,N)$ outcomes of the joint distribution.