Pr(W = w, B = b, G = g)
where w + b + g = 20.
You could also build in the w + b + g = 20 restriction and write the pmf as:
Pr(W = w, B = b, G = g) .
And, I hate to say it, but the jury question you posted a while ago will also follow a multivariate hypergeometric distribution since (I assume) there's no replacement after each juror is selected. The card one too - if there's no replacement. I've added a reply noting this to each of those threads.