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A college admissions committee will grant a certain number

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sset009
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A college admissions committee will grant a certain number [#permalink] New post   28 Aug 2008, 06:58
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.
let the answers begin!!!



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Re: A college admissions committee will grant a certain number [#permalink] New post   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.
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Re: A college admissions committee will grant a certain number [#permalink] New post   Updated on: 28 Aug 2008, 21:13
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.
let the answers begin!!!


I messed it up :)

Originally posted by amitdgr on 28 Aug 2008, 08:47.
Last edited by amitdgr on 28 Aug 2008, 21:13, edited 2 times in total.
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asdert
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Re: A college admissions committee will grant a certain number [#permalink] New post   29 Aug 2008, 09:06
I agree on both answers. I solved just like KASSALMD but I liked x2suresh's approach.
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GMBA85
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Re: A college admissions committee will grant a certain number [#permalink] New post   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.
let the answers begin!!!


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?
Many thanks in advance!
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bhushangiri
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Re: A college admissions committee will grant a certain number [#permalink] New post   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?
Many thanks in advance!



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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Re: A college admissions committee will grant a certain number [#permalink]
07 Sep 2008, 05:04
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