Problem 2

[anwarma]

A 4 person task force is to be formed from the 4 men and 3 women who work in a COMPANY G' HR dept. 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 <<--ANSWER
(C) 35
(D) 56
(E) 144

I am not sure how answer is 18.

[egybs]

We need to choose 2 men out of 4 men and 2 women out of 3 women. So we have the following combination that needs to occur:

4C2 * 3C2 = 18

Check out this excellent article on Permutations and Combinations:
https://www.mansw.nsw.edu.au/members/ref ... no4yen.htm

[rosh26]

Hi Can you do the mathamatical computation to this answer?

Or even factorials would work...thanks...

[egybs]

sure -

4C2 = 4!/(2!*(4-2)!) = 24/4 = 6

3C2 = 3!/(2!*(3-2)!) = 6/2 = 3

6*3=18

[amirp]

it seems like we ignore the part that says "A 4-person task force is to be formed..." . would the answer be the same if the question asked for "A 5-person task force is to be formed ... "?

can anyone clarify this?

[ketandoshi]

Amirp,

We are not neglecting "4 -person" as the task force has 2 men and 2 women (4C2* 3C2) if you had "5 -person" then it may ask as 3 men & 2 women or 2 men & 3 women. If I am wrong please somebody correct me.

[amirp]

ohhhh, I see. you are correct. We are considering it, but in an indirect way.

thanks

[likithae]

Amirp,

We are not neglecting "4 -person" as the task force has 2 men and 2 women (4C2* 3C2) if you had "5 -person" then it may ask as 3 men & 2 women or 2 men & 3 women. If I am wrong please somebody correct me.

yes..... you are correct.......