If we had 6 red balls and 6 green balls(all enumerated), and if we were randomly picking the pair of those balls, the probability of having 3 pairs of red balls only would be computed by the following formulae: (6!/((2!)^3 3!)^2 / (12!/((2!)^6 6!) I do not however know for sure how would one find the probability of picking other variations, such as pairs of one red and one green ball, or 2 pairs of one green and one red ball and the remaining pairs being all red and all green. I would appreciate some insight on how to determine the right formulae to use.