Joint Probability Question

Hi, I am having trouble with the following question:

Five balls are drawn without replacement from an urn containing 7 blue balls, 4 green balls, and 8 yellow balls. Let B, G, and Y be the total number of blue, green and yellow balls drawn, respectively. Find

a) The joint probability mass function of B, G, and Y.

b) The joint probability mass function of Y and B

c) THe marginal probability mass function for B, G, and Y separately. Do these marginal probabilities look familiar? ID them.

For a) I tried modelling the joint probability mass function using a combinatorial approach.

c(7 choose B)c(4 choose G)c(8 choose Y)/c(19 choose 5).

And B+G+Y=5 (because you can only choose 5 balls). However, after this I'm stuck.