Question

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 forme?

Answer 1

Answer:

Total 18 task force can be formed.

Step-by-step explanation:

Total number of men = 4

Total number of women = 3

We need to form a 4-person task force.

The total number of ways of selecting r items from n items is

$^nC_r=\frac{n!}{r!(n-r)!}$

Total number of ways of selecting 2 men from 4 men = $^4C_2$

Total number of ways of selecting 2 women from 3 men = $^3C_2$

Total number of different task forces that can be formed is

$Total=^4C_2\times ^3C_2$

$Total=\frac{4!}{2!(4-2)!}\times \frac{3!}{2!(3-2)!}$

$Total=\frac{4!}{2!2!}\times \frac{3!}{2!1!}$

$Total=\frac{4\times 3\times 2!}{2\times 1\times 2!}\times \frac{3\tmes 2!}{2!}$

Cancel out common factors.

$Total=6\times 3$

$Total=18$

Therefore total 18 task force can be formed.