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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MGMAT says the answer to this is C.
I thought statement 1 was sufficient by itself because if you know the amount of scholarship winners, then you know the amount of scholarship losers - so 10!/6!4! yields the amount of possible winner combinations...Assuming I'm entirely off, what does 10!/6!4! tell you in relation to this problem?
Thanks.
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3 postsPage 1 of 1
- AarondoesSA
I agree with you, I also thought A was sufficient. The question is asking for "how many different ways can the committee dole out the scholarships among the pool of 10 applicants?"...I don't understand why it necessarily needs to be clarified which person gets which type of scholarship. I thought with condition (1) the total # of ways is equal to 10C6 * 3!
I added the 3! b/c I thought we then had to account for the 3 different types of scholarships..could a MGMAT instructor or someone else please explain?
The supplied answer in the test goes off the anagram format, maybe that's why I just can't understand why Condition (1) isn't correct.
Thanks,
Aaron
I added the 3! b/c I thought we then had to account for the 3 different types of scholarships..could a MGMAT instructor or someone else please explain?
The supplied answer in the test goes off the anagram format, maybe that's why I just can't understand why Condition (1) isn't correct.
Thanks,
Aaron
- JonathanSchneider
- ManhattanGMAT Staff
- Posts: 370
- Joined: Sun Oct 26, 2008 3:40 pm
Actually, I think the answer could be A as well, but not for the reasons that either of you indicated.
(10!)/(6!*4!) would be the number of ways that we could choose six people out of ten. However, note that this problem asks us how many ways to dole out the scholarships. Well, we haven't yet determined what types of scholarships we will be giving out. So you would have to look at the various breakdowns: what if we give out four $10K scholarships, and only one of each of the other kinds? That will result in a certain number of options for doling out the money. Likewise, what if we were to take two scholarships of each level?
The official answer for this problem relies on you seeing that because we do not yet know the breakdown of what type of scholarhips we are giving out, we cannot solve. My personal beef with that is that we could simply add up all of the possibilities, to show the total number of possibilities. (AKA, the # of options when we have 4/1/1, the number of options when we have 2/2/2, etc.) But this is just due to the wording of the question, which could be cleaned up a bit, imho.
(10!)/(6!*4!) would be the number of ways that we could choose six people out of ten. However, note that this problem asks us how many ways to dole out the scholarships. Well, we haven't yet determined what types of scholarships we will be giving out. So you would have to look at the various breakdowns: what if we give out four $10K scholarships, and only one of each of the other kinds? That will result in a certain number of options for doling out the money. Likewise, what if we were to take two scholarships of each level?
The official answer for this problem relies on you seeing that because we do not yet know the breakdown of what type of scholarhips we are giving out, we cannot solve. My personal beef with that is that we could simply add up all of the possibilities, to show the total number of possibilities. (AKA, the # of options when we have 4/1/1, the number of options when we have 2/2/2, etc.) But this is just due to the wording of the question, which could be cleaned up a bit, imho.
3 posts Page 1 of 1