Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2008 / Paper 2 / 11 / a / i / Solution

Every set of $S$ students is equally likely to be the specified college. There are $\left(\genfrac{}{}{0ex}{}{N}{S}\right)$ choices in total and $\left(\genfrac{}{}{0ex}{}{L}{S}\right)$ choices consisting entirely of the specified group. Therefore the hypergeometric distribution gives