# Combinations with committees

I have the following question.

A business has 30 female workers, 3 of which are in a management position. It has 150 total men, 12 of which are in a management position. A committee consisting of three men and three women is to be created. How many different committees can be created if the committee has to include at least one member from management.

I'm getting stuck on the requirements of three men and three women. If it were just 6 people without gender constraints I fully understand. Any help with how to approach this would be greatly appreciated.

I had the initial thought of determining total possible number of 3 male and 3 female committees C(30,3)*C(150,3) minus then committees with no management C(27,3)*C(138,3)..but I'm not confident in this.

Thanks

• Your approach of subtracting the number of committees with three men and three women who contain no members of the management from the total number of committees with three male and three female members yields the correct solution. – N. F. Taussig Dec 15 '16 at 23:39