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# I have tried a couple of iterations of this problem and

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Manager
Joined: 17 Mar 2007
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Location: San Francisco, CA
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I have tried a couple of iterations of this problem and [#permalink]

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05 Aug 2008, 22:03
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I have tried a couple of iterations of this problem and still cannot get the answer of 100. Any help?
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_________________

Death is not the greatest loss in life. The greatest loss is what dies inside us while we live.
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Kudos [?]: 22 [0], given: 3

Director
Joined: 23 Sep 2007
Posts: 782

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Re: GMATPrep - Combination question [#permalink]

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05 Aug 2008, 22:18
you can have a committee of 3 frenchs or 2 frenches + 1 other, or 1 french + 2 others.

1 french + 2 others --> you get 4 choices among the french and 2 among the 6 others
so 6C2 = 15
15 * 4 = 60

2 frenches + 1 other --> you get 6 choices among the others, and 2 among the 4 frenches
so 4C2 = 6
6 * 6 = 36

3 frenches --> 3 among the 4 frenches
so 4C3 = 4

60 + 36 + 4 = 100

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Current Student
Joined: 18 Jun 2008
Posts: 225

Kudos [?]: 59 [0], given: 3

Re: GMATPrep - Combination question [#permalink]

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05 Aug 2008, 22:22
miccarlo wrote:
I have tried a couple of iterations of this problem and still cannot get the answer of 100. Any help?

10 ppl
4 teach only french
6 teach only other

need a team of 3 with at least 1 french teacher
so we have to sum the following:
choose 1 from 4 and 2 from 6
choose 2 from 4 and 1 from 6
choose 3 from 4 and 0 from 6
=>
4*15
6*6
4
=>
60+36+4=100

Kudos [?]: 59 [0], given: 3

Manager
Joined: 17 Mar 2007
Posts: 126

Kudos [?]: 22 [0], given: 3

Location: San Francisco, CA
Schools: Haas, Booth, Kellogg, Stanford
Re: GMATPrep - Combination question [#permalink]

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05 Aug 2008, 22:51
Makes sense...not sure why I always try to take the hard way around to calculate these combination questions...better to think about the question first before trying calculations. Thanks!
_________________

Death is not the greatest loss in life. The greatest loss is what dies inside us while we live.
- Norman Cousins

Kudos [?]: 22 [0], given: 3

Director
Joined: 12 Jul 2008
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Schools: Wharton
Re: GMATPrep - Combination question [#permalink]

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05 Aug 2008, 22:55
miccarlo wrote:
I have tried a couple of iterations of this problem and still cannot get the answer of 100. Any help?

Total number of ways to choose 3 members out of 10 people: 10 choose 3 = 120
Total number of ways to choose 3 members that do not include a french teacher: 6 choose 3 = 20

Total number of ways to choose 3 members with at least 1 french teacher = 120 - 20 = 100

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Manager
Joined: 09 Jul 2008
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Location: Dallas, TX
Schools: McCombs 2011
Re: GMATPrep - Combination question [#permalink]

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07 Aug 2008, 18:06
Could you please tell me what I am messing up here:

For the first spot, we can pick from 4 choices. For the second spot, we can pick from the remaining 9 choices.

I did 4C1 X 9C2 = 116

Evidently this is incorrect, but I can't figure why

Kudos [?]: 42 [0], given: 1

Re: GMATPrep - Combination question   [#permalink] 07 Aug 2008, 18:06
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