nverma 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?
(1) In total, six scholarships will be granted.
(2) An equal number of scholarships will be granted at each scholarship level.
Statement 1: Total 6 scholarships granted, hence we need 6 students to receive these scholarships.
6 students can be chosen out of 10 students in 10C6 ways.
However we do not know which & how many of each scholarships are granted.
Statement 1 is Not Sufficient.
Statement 2: Equal number of scholarships from each level are granted.
We do not know the exact number of each scholarship from each level.
Statement 2 is Not Sufficient.
Combining we get, 6 scholarships given out & equal # of each of the 3 levels. Hence 2 scholarships from each level.
Now 6 students are selected out of 10 in 10C6 ways.
We can select 2 students out of the 6, to receive 2 scholarships in 6C2
Similarly 2 from remaining 4 students in 4C2 ways
& lastly we give out the final 2 scholarships to the 2 remaining students in 2C2 ways.
Total # of ways to give out the scholarships = 10C6 * 6C2 * 4C2 * 2C2
Combining is Sufficient.
Answer C.
Thanks,
GyM
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