Each year, a college admissions committee grants a certain number of $10,000 scholarships, $5,000 scholarships, and $1,000 scholarships. The number of scholarships granted at each level does not vary from year to year, and no student can receive more than one scholarship. This year, how many different ways can the committee distribute 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.


The displayed answer is (C)

I guess I don't understand why you need statement (2). Obviously only knowing the applicant pool count and the denominations of the scholarships is insufficient because you could distribute an infinite number of scholarships (the combo inst countable) So I had rephrased the question as "how many scholarships were given out". Obviously (1) answers that question.

Just looking at the possibilities, label the applicants as a...j you could...

Give 6, 10000 scholarships to a
Give 5, 10000 scholarships to a and 1, 10000 scholarship to b

And so on, with just 10000 scholarships. Then do the same with 5000, same with 1000, and then any mixtures. I don't know what the result will be (probably large) but its finite and is thus sufficient.

Can someone point to the hole in my logic here?

Please check out this thread and let us know if we can help further: mgmat-college-scholarship-t7253.html

_________________
Jamie Nelson
ManhattanGMAT Instructor