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Totally bowled out

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Intern
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Joined: 04 Nov 2007
Posts: 45
Totally bowled out  [#permalink]

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New post 14 Jan 2009, 06:50
find the no. of ways of selecting a comittee of 5 from 4 man and 4
women.the commitee consist of one president one vice president and 3
secretaries. the comitee shud have at the max 2 women and having at the
max one woman holding one of the two posts on the committee.
plz clearly elaborate the answer

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Joined: 12 Aug 2008
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Re: Totally bowled out  [#permalink]

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New post 14 Jan 2009, 11:14
Either am way off on this or this is the right answer and there HAS to be a shorter way.

Scenario 1: 4 men and 1 woman secretary.

President can be selected in 4C1 ways; VP can be selected in 3C1 ways; 1 woman Secretary in 4C1 ways and the remaining two secretaries in 2C2 ways.
=4*3*4*1=48

Scenario 2: 3 men and 2 women secretaries.

President can be selected in 4C1 ways; VP can be selected in 3C1 ways; 2 woman Secretaries in 4C2 ways and the remaining secretary in 2C1 ways.
=4*3*6*2=144

Scenario 3: 1 woman President, 1 male VP, 2 male secretaries and 1 woman secretary

President can be selected in 4C1 ways; VP can be selected in 4C1 ways; 1 woman Secretary in 3C1 ways and the two male secretaries in 3C2 ways.
=4*4*3*3=144

Scenario 4: 1 male President, 1 woman VP, 2 male secretaries and 1 woman secretary

President can be selected in 4C1 ways; VP can be selected in 4C1 ways; 1 woman Secretary in 3C1 ways and the two male secretaries in 3C2 ways.
=4*4*3*3=144

Total number of ways is the sum of all scenarios:

48+144+144+144
=480
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Re: Totally bowled out  [#permalink]

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New post 14 Jan 2009, 11:25
My Ans: 256 ways.

(ways to find 2 men for chairs)*(ways for 2M1W + ways for 2M2W) + (ways to find 1m1W for chairs)*(ways for 3M + ways for 2M1W)

i.e.

4C2*(2C2*4C1 + 2C2*4C2) + 4C1*4C1*(3C3 + 3C2*3C1) = 256.

Whais is the OA?
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Re: Totally bowled out  [#permalink]

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New post 15 Jan 2009, 09:18
I do not know the OA.

Is the question framed wrong? I copied it from one of the forum emails that discusses GMAT.

--== Message from GMAT Club Team ==--

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Re: Totally bowled out &nbs [#permalink] 15 Jan 2009, 09:18
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