Suppose you have an urn with 2 yellow balls, 3 red balls, 6 white balls, and 12 blue balls. You randomly draw 4 balls from the urn without replacement. Given that at least one of the balls is yellow, what is the probability that all 4 balls will be different colors?

I know that you have to use Bayes' rule, with P(B|A) = 1 because if you have 4 colors, one of them must be yellow. But I'm not sure about the different probabilities.

I think P(A) might be 2 choose 1 + 3 choose 1 + 6 choose 1 + 12 choose 1 all divided by 23 choose 4, but I"m not sure. And I don't know how to get P(>= 1 yellow).Any one have any idea?

Thanks!