Answer: The required number of different possible committees is 81172.
Step-by-step explanation: Given that a department contains 9 men and 15 women.
We are to find the number of different committees of 6 members that are possible if the committee must have strictly more women than men.
Since we need committees of 6 members, so the possible combinations are
(4 women, 2 men), (5 women, 1 men) and (6 women).
Therefore, the number of different committees of 6 members is given by
Thus, the required number of different possible committees of 6 members is 81172.