A scientific committee of 4 persons is to be randomly selected from a group consisting of 3 biologists, 3 physicists and 4 mathematicians. Let X denote the number of biologists, Y the number of physicists and Z the number of mathematicians on the committee.
What is the the joint probability mass function of the random vector (X,Y,Z) ?
Unfortunately I do not have enough reputation to put this in a comment. I am currently working on this problem as part of a problem set, but I would suggest the following: In order to find the joint probability mass function of a vector we can follow the chain rule of random variables. The chain rule of random variables with regards to the joint probability mass function for discrete values is as follows in the general form:
Which can be found on the wikipedia page: http://en.wikipedia.org/wiki/Joint_probability_distribution
While this isn't a thorough answer, I hope it benefits you forming a proper approach.