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# A college admissions committee will grant a certain number

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Manager
Joined: 14 Jun 2008
Posts: 162

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28 Aug 2008, 06:58
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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? given that

problem number 1)
there are two of each type

problem number 2)
there are 1 x \$10000, 2 x \$50000, 3 x \$1000

this question came to mind when i was solving a similar DS.
what confused me was in my approach, the order of handing out scholarships seemed to matter. hopefully someone can clear my doubt

no OA.
Manager
Joined: 22 Jul 2008
Posts: 144

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28 Aug 2008, 07:23
Problem 1: 10 C 2 * 8 C 2 * 6 C 2 = 18,900 ways.

Problem 2: 10 C 1 * 9 C 2 * 7 C 3 = 12,600 ways.
VP
Joined: 30 Jun 2008
Posts: 1019

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28 Aug 2008, 08:47
sset009 wrote:
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? given that

problem number 1)
there are two of each type

problem number 2)
there are 1 x \$10000, 2 x \$50000, 3 x \$1000

this question came to mind when i was solving a similar DS.
what confused me was in my approach, the order of handing out scholarships seemed to matter. hopefully someone can clear my doubt

no OA.

I messed it up
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Last edited by amitdgr on 28 Aug 2008, 21:13, edited 2 times in total.
Senior Manager
Joined: 09 Oct 2007
Posts: 459

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29 Aug 2008, 09:06
I agree on both answers. I solved just like KASSALMD but I liked x2suresh's approach.
Manager
Joined: 03 Jun 2008
Posts: 131
Schools: ISB, Tuck, Michigan (Ross), Darden, MBS

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07 Sep 2008, 01:13
x2suresh wrote:
sset009 wrote:
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? given that

problem number 1)
there are two of each type

HHMMLL
1 2 3 4 5 6 7 8 9 10

=10C6 *6!/2!2!2! = 210* 90 = 18900

problem number 2)
there are 1 x \$10000, 2 x \$50000, 3 x \$1000

HHHMML
1 2 3 4 5 6 7 8 9 10
=10C6 *6!/3!2 =210*60 = 12600

this question came to mind when i was solving a similar DS.
what confused me was in my approach, the order of handing out scholarships seemed to matter. hopefully someone can clear my doubt

no OA.

x2suresh could you please explain the 6!/3!2 or 6!/2*2*2 bit? How do we get this? What is the logic behind this?
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Manager
Joined: 15 Jul 2008
Posts: 205

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07 Sep 2008, 05:04
GMBA85 wrote:

x2suresh could you please explain the 6!/3!2 or 6!/2*2*2 bit? How do we get this? What is the logic behind this?

6! is the number of ways of arranging the 6 chosen people. But of the 6 when there are 3 of type1, 2 of type2 and 1 of type3.. then the actual number of arranging the 6 chosen people is 6! / 3!*2!*1!

when there are 2 of each type, then it becomes 6! / 2!*2!*2!

here the types represent the number of each type of schol available.
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# A college admissions committee will grant a certain number

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