Problem Solving

A 4-person task force is to be formed from 4 men and 3 women who work in Comany G's human resource department. If there are to be 2 men and 2 women on the task force, how many different task forces can be formed?

14
18 *Correct*
35
56
144


If someone could help me out I would appreciate it very much. Thank you.

This is a two stage combination problem (we know its combination because the order doesn't matter).

First we want to find out, out of 4 candidates, how many combinations of 2 men there are:

Ans = N!/(k!(N-k)!) = 4!/(2!(4-2)!) = 6 different men combinations

Second, we want to calculate, out of 3 candidates, how many women combinations there are:

(same formula) = 3!/(2!(3-2)1) = 3

Since each man combo can have any of the 3 woman combination, we multiply to get 18 total different combinations.

Hope this helps, good luck.