In this problem we consider how many ways there are to divide a set of n distinct students into k distinct
study groups. As an example, if we have students {a, b, c} and two groups {I, J} then there are precisely
6 ways to divide the students such that each group contains at least one student. Explicitly we then have
then have the follwing pairings
{a, b}I {c}J , {a, c}I {b}J , {a}I {b, c}J , {c}I {a, b}J , {b}I {a, c}J , {b, c}I {a}. (a) Find the general formula f(n, k) for the number of ways to divide n distinct students into k distinct
groups, where each group contains at least one student.
(b) Compute (n, k) = (9 + (x mod 5), 3 + (x mod 2)), where x is 9.