Given n items (20% type A, 80% type B), I'm looking for a way to distribute them randomly into g groups of equal size. It must be possible for one group to end up with As in the majority but it must not be inevitable. I.e. If I was using binomial distribution, it would be extremely unlikely (with large values of n) to get a group in which the proportion of As was far from 20%. With uniform distribution between 0 and n/g, the first group to which As were allocated would almost always get many more As than the other groups (because the mean of the distribution function would be 50% rather than 20%).
I don't know much about stats and probability so this may be a stupid question but I suppose what I am asking for is a distribution function whose mean is 0.2 but which is likely to generate numbers between 0 and 0.2 and numbers between 0.2 and 1 with equal probability as well.