Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / 18 / a / Solution

All size-six subsets are equally likely under uniform sampling without replacement. There are $\left(\genfrac{}{}{0ex}{}{12}{6}\right)$ subsets in total, and $\left(\genfrac{}{}{0ex}{}{6}{3}\right)\left(\genfrac{}{}{0ex}{}{6}{3}\right)$ contain the required three members from each group. Thus the hypergeometric distribution gives