Bunuel wrote:

derekgmat wrote:

In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96

(B) 125

(C) 155

(D) 175

(E) 225

Alternatively one can do:

The total number of committees of 3 possible out of 12 people without restrictions: \(C^3_{12}=220\);

The number of committees with all men: \(C^3_5=10\);

The number of committees with all women: \(C^3_7=35\);

Thus the answer is 220-(10+35)=175.

Answer: D.

To make this question clearer, i think it should be stated more precisely "

exactly 2 of them are of the same gender" otherwise one could understand that commetees consisting of just men and/or just women are possible. Don't you think so Bunuel?

_________________

If you found my post useful and/or interesting - you are welcome to give kudos!