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A five-member committee is to be formed from a group of five

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SVP
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Joined: 21 Jul 2006
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A five-member committee is to be formed from a group of five [#permalink] New post 24 Aug 2008, 10:12
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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
Manager
Manager
Joined: 15 Jul 2008
Posts: 210
Followers: 3

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GMAT Tests User
Re: PS: Permutations [#permalink] New post 24 Aug 2008, 10:28
tarek99 wrote:
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


you can have either (3 Military and 2 civilians) or ( 2 military and 3 civilians)

so (5C3 * 9C2) + (5C2*9C3) = 1200
Intern
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Joined: 20 Aug 2008
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Re: PS: Permutations [#permalink] New post 24 Aug 2008, 10:35
Hi Tarek,

I believe it should be 1200.

The way to get it is well.

We can arrange in these two ways M = Military and C = Civilians
MMCC? => MMCCC or MMCCM
= Case 1 + Case2

=2 out of 5 military and 3 out of 9 military + 3 out of 5 military and 2 out of nine civilians

= 5C2 * 9C3 + 5C3*9C2

= 5*4* 9*8*7 5*4*3* 9*8
--------------- + ---------------
2* 3*2 3*2 * 2

= 840 + 360
= 1200

-Max
SVP
SVP
Joined: 21 Jul 2006
Posts: 1550
Followers: 7

Kudos [?]: 152 [0], given: 1

GMAT Tests User
Re: PS: Permutations [#permalink] New post 24 Aug 2008, 11:26
OA is B. Thanks guys
Re: PS: Permutations   [#permalink] 24 Aug 2008, 11:26
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