Combinatorics Problem: Employee grouping problem # Problem A company employs eight people in the marketing department, five in the manufacturing department and three in the financing department. A project team of six is to be formed. In how many ways can the team to be formed if: 1. there are to be two representatives from each department? 2. there are at least two members from the marketing department? # My Attempt For the first question, I was able to do it: $$5 × 4 × 24 × 23 = 11040.$$ However, I am unable to get the second question. I tried $$16 × 15 × 14 × 13 × 12 × 11$$ but that is wrong. What am I doing wrong? How would I go about solving these kinds of problems.

No restrictions: $\displaystyle \binom{16}{6}$

No member is from marketing department: $\displaystyle \binom{8}{6}$

Exactly one member is from marketing department: $\displaystyle \binom{8}{1}\binom{8}{5}$

At least two members are from marketing department: $\displaystyle \binom{16}{6}-\binom{8}{6}-\binom{8}{1}\binom{8}{5}=7532$