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# A college admissions committee will grant a certain number

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Manager
Joined: 28 Jul 2004
Posts: 135
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth

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21 Dec 2008, 05:52
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A college admissions committee will grant a certain number of \$10,000 scholarships, \$5,000 scholarships, and \$1,000 scholarships. If no student can receive more than one scholarship, how many different ways can the committee dole out the scholarships among the pool of 10 applicants?

(1) In total, six scholarships will be granted.

(2) An equal number of scholarships will be granted at each scholarship level.

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kris

VP
Joined: 17 Jun 2008
Posts: 1474

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21 Dec 2008, 12:44
D.

From stmt1: 10C6.

From stmt2: total number of scholarships could be 3, 6 or 9.
Hence, total number = 10C3 + 10C6 + 10C9.
Director
Joined: 01 Apr 2008
Posts: 821
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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24 Dec 2008, 05:34
I think it should be D.
1> 10C6 will give all possible combinations of distributing 6 scholarships among 10 people but we dont know which of these are valid as per the clause "one person can get only one type of scholarship". So we cant find the right number of combinations.

2> here we dont know how many scholarships will be granted.

Taking 1 and 2, we know that the only possible combination is 2,2,2.
What is OA?
Manager
Joined: 15 Apr 2008
Posts: 159

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24 Dec 2008, 11:47
Economist wrote:
I think it should be D.
1> 10C6 will give all possible combinations of distributing 6 scholarships among 10 people but we dont know which of these are valid as per the clause "one person can get only one type of scholarship". So we cant find the right number of combinations.

2> here we dont know how many scholarships will be granted.

Taking 1 and 2, we know that the only possible combination is 2,2,2.
What is OA?

i think you mean C

combinations can be like this 10C2+ 8C2+6C2
Manager
Joined: 21 Dec 2008
Posts: 70

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28 Dec 2008, 07:09
its clear C

10C2+ 8C2+6C2 - right

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

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