My question concerns a variant of the classic urn problem for the case of more than 2 types (colours).
Given a single urn with $N$ balls of 3 distinct colours (say, red ($R$), green (G) and blue ($B$)), one employs the multivariate hypergeometric distribution to compute the probability $P(RGB)$ of sampling three balls without replacement, and observing exactly one ball of each colour.
I'm interested to know if there is a multivariate probability distribution for the case of $multiple$ urns.
More specifically, is there a distribution that accounts for the correlation of types (colours) of balls among $N$ urns? I suppose one can think of it as a sort of $spatial$ multivariate urn problem.
I've not been able to find anything on this site nor through a simple Google search.