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# A test maker is to design a probability test from a list of

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A test maker is to design a probability test from a list of [#permalink]

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07 Oct 2009, 05:57
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A test maker is to design a probability test from a list of 21 questions. The 21 questions are classified into three categories: hard, intermediate and easy. If there are 7 questions in each category and the test maker is to select two questions from each category, how many different combinations of questions can the test maker put on the test?

A) 3*(7!/(5!2!))
B) 3*(7!/(5!))
C) 3*(7!/(2!))
D) 3*21
E) 72
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Re: Test maker - combinations problem [#permalink]

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07 Oct 2009, 06:41
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Expert's post
mendelay wrote:
A test maker is to design a probability test from a list of 21 questions. The 21 questions are classified into three categories: hard, intermediate and easy. If there are 7 questions in each category and the test maker is to select two questions from each category, how many different combinations of questions can the test maker put on the test?
A) 3*(7!/(5!2!))
B) 3*(7!/(5!))
C) 3*(7!/(2!))
D) 3*21
E) 72

There is no correct choice!

The number of combinations will be C(2,7)*C(2,7)*C(2,7)=C(2,7)^3=21^3=9261

Check the source. A and C give the same answers.
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Joined: 21 Jul 2009
Posts: 265
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Re: Test maker - combinations problem [#permalink]

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07 Oct 2009, 06:59
The question is from PlatinumGmat http://www.platinumgmat.com/practice_gm ... on_id=2252
and the OA given there is A.

However, I disagree because 7C2*7C2*7C2 ≠ 37C2.
I think the answer is none of the above.
Math Expert
Joined: 02 Sep 2009
Posts: 35951
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Kudos [?]: 90128 [1] , given: 10418

Re: Test maker - combinations problem [#permalink]

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07 Oct 2009, 07:05
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Expert's post
mendelay wrote:
The question is from PlatinumGmat http://www.platinumgmat.com/practice_gm ... on_id=2252
and the OA given there is A.

However, I disagree because 7C2*7C2*7C2 ≠ 37C2.
I think the answer is none of the above.

They made a mistake: 7C2*7C2*7C2 ≠ 37C2 its (7C2)^3=9261. There must be a typo.
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Re: Test maker - combinations problem [#permalink]

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15 Nov 2013, 05:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Test maker - combinations problem   [#permalink] 15 Nov 2013, 05:06
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