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

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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]  24 Aug 2008, 10:12
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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
Joined: 15 Jul 2008
Posts: 209
Followers: 3

Kudos [?]: 27 [0], given: 0

Re: PS: Permutations [#permalink]  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
Joined: 20 Aug 2008
Posts: 29
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Re: PS: Permutations [#permalink]  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
Joined: 21 Jul 2006
Posts: 1551
Followers: 8

Kudos [?]: 287 [0], given: 1

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