An urn contains three white, six red, and five black balls. Six of these balls are randomly selected without replacement from the urn. Let X and Y denote the number of white and black balls selected respectively. Compute the conditional probability function of X given that Y = 3. Also compute E[X given that Y = 1].

I would love some help on this problem.

I know if Y = 3, the probability that no white balls are selected is (8/11)(7/10)(6/9). I'm not really sure what to do after this. Thanks for your help.