A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?
a. 14
b. 18
c. 35
d. 56
e. 144
My answer would be that n = 4*3*3*2, but 72 does not exist as a possible answer. GMATPrep marks b: 14, which obviously is 4*2+3*2, as the correct answer, and I do not understand how this can be the correct answer (say: I disagree).
I have 4 positions available in the team. The first can be taken by one of the 4 men, the second by one of the remaining 3 men, the third by one of the 3 women, and the fourth by one of the remaining 2 women, thus 4*3*3*2.
Even if I break the problem up into two smaller problems, asking how many different men task forces and women task forces I can build, which, as it seems, the GMATPrep answer does, I do not understand why the resulting combinations would be added up rather than multiplied. I can build 4*3 different men task forces, and 3*2 different women task forces, and combining each of them I can build 12*6 different mixed task forces.
Please help clarifying the answer.
a. 14
b. 18
c. 35
d. 56
e. 144
My answer would be that n = 4*3*3*2, but 72 does not exist as a possible answer. GMATPrep marks b: 14, which obviously is 4*2+3*2, as the correct answer, and I do not understand how this can be the correct answer (say: I disagree).
I have 4 positions available in the team. The first can be taken by one of the 4 men, the second by one of the remaining 3 men, the third by one of the 3 women, and the fourth by one of the remaining 2 women, thus 4*3*3*2.
Even if I break the problem up into two smaller problems, asking how many different men task forces and women task forces I can build, which, as it seems, the GMATPrep answer does, I do not understand why the resulting combinations would be added up rather than multiplied. I can build 4*3 different men task forces, and 3*2 different women task forces, and combining each of them I can build 12*6 different mixed task forces.
Please help clarifying the answer.
