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# From a group of eight people how many different committees

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Manager
Joined: 24 Jun 2003
Posts: 91
Location: Moscow
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From a group of eight people how many different committees [#permalink]  08 Aug 2003, 00:07
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From a group of eight people how many different committees of four or five people each can be arranged?
Manager
Joined: 10 Jun 2003
Posts: 210
Location: Maryland
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Committee of four: 8C4 = 70
Committee of five: 8C5 = 56

Then four or five would be 70 + 56 = 126
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
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Shouln't the answer be 8C4 * 2 + 8C5 ?

The question is asking for number of committees Not the number of ways to form the committees

Thanks
Director
Joined: 03 Jul 2003
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gmatblast wrote:
Shouln't the answer be 8C4 * 2 + 8C5 ?

The question is asking for number of committees Not the number of ways to form the committees

Thanks

Could you explain the reason for multiplying by 2?
Director
Joined: 13 Nov 2003
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Why not 350? 8C4=70, choose one more from the rest 4 to form a five member committee or 70x4=280-5 member committees and 70-4 memeber or 350 in total.
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
Followers: 1

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

gmatblast wrote:
Shouln't the answer be 8C4 * 2 + 8C5 ?

The question is asking for number of committees Not the number of ways to form the committees

Thanks

Could you explain the reason for multiplying by 2?

That was my mistake!! We do not need to multiply by 2.

I overthought the problem. I thought that the question is asking for number of committees Not the number of ways to form the committees

So I thought when we select any 4 people out of 8 to form a commitee, we are basically creating 2 committees. 4 selected people and 4 remaining. So we need to multiply 8C4 by 2. But I now know that 8C4 will cover all the remaining people as well.

So no need to multiply by 2.
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