Answer :
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
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Total number of ways of selecting 2 men from 4 men = [tex]^4C_2[/tex]
Total number of ways of selecting 2 women from 3 men = [tex]^3C_2[/tex]
Total number of different task forces that can be formed is
[tex]Total=^4C_2\times ^3C_2[/tex]
[tex]Total=\frac{4!}{2!(4-2)!}\times \frac{3!}{2!(3-2)!}[/tex]
[tex]Total=\frac{4!}{2!2!}\times \frac{3!}{2!1!}[/tex]
[tex]Total=\frac{4\times 3\times 2!}{2\times 1\times 2!}\times \frac{3\tmes 2!}{2!}[/tex]
Cancel out common factors.
[tex]Total=6\times 3[/tex]
[tex]Total=18[/tex]
Therefore total 18 task force can be formed.