Chance of x Red balls sharing a bucket with a Green ball

[Superposed_Cat]

If I have 237 buckets, and there are n green balls distributed randomly over those buckets, and I put 34 new red balls randomly in those 237 buckets, what is the formula for the probability that x green balls share a bucket with a red ball?

Any help appreciated.

 

[BvU]

Homework ? Then we need an attempt from you in order to estimate what kind of advice is most effective.

What do you know of permutations and combinations ?