DS on committe

[ruplun]

A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?
A. 119

B. 1,200

C. 3,240

D. 3,600

E. 14,400

Please solve

[clock60]

it is better to send in PS section but anyway
we have two possible committees
2-officers and 3-civilian
3-officers and 2 civilian
5C2*9C3+5C3*9C2=840+360=1200
my answer B

[maihuna]

or : 2 army 3 civ = 5c2*9c3 = 10*9*8*7/3*2 = 10*3*4*7= 840
3 army 2 civ = 5c3*9c2 = 10*9*8/2 = 360

total 1200
B. 1,200

[ruplun]

thanks a lot

[lip3]

Hi, I'm not really sure why that is the answer. I see that it is "at least", so there could be 2,3,4,5 army or 2,3,4,5 civilian... Can someone provide the reason behind the approach. I just thought it could be 5c2*13C3...(which is not correct)

Patrick

[Brent@GMATPrepNow]

Hi, I'm not really sure why that is the answer. I see that it is "at least", so there could be 2,3,4,5 army or 2,3,4,5 civilian... Can someone provide the reason behind the approach. I just thought it could be 5c2*13C3...(which is not correct)

Patrick

The question say that the [5-person]committee must include at least two officers and two civilians

Your suggestion that there could be 5 civilians would mean that there are zero military officers, and this would break the restriction that there must be at least two officers.

I think you're reading the restriction as the committee must include at least two officers OR two civilians