Combinatorics DS

crak.gmat 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.


Combinatorics is where I am weak, would really appreciate a response with explanations. Thanks!

OA C

To allay your fear of combinatorics, remember that you don't have to calculate the value..you have to tell whether the data is sufficient to calculate the value

The data we require to get all possible combinations is

1) How many EACH (5k, 1k etc..)type of scholarship are present because if we know this value for each type, we can calculate the value for different ways to distribute among 10 student (given value)

Stmt 1 -> gives total number of scholarship => 6
Stmt 2 -> equal number of each type of scholarship are to be given.

so, we have 2 scholarship of each type from 1st and 2nd.

Hence, we have answer to the question above, that we can calculate the values from given data

NOTE - we didn't had to calculate the values

isn't it A?

first one tells that order is important as one student can have only one scholarship.
so, number of ways : 10P6

second one doesn't states how many schols to be given and therefore we cant determine how many each type of schols would be given here.

So, A is sufficient for the answer here.

PS: i too am not concrete in PnC though

I too think A is sufficient here. 10P6
B does not give us the exact number of prizes which could either be 2 or 3 per scholarship.

Can the experts Ian or Stuart please help with this one?

In my opinion, A is not sufficient.
We'll be able to know what combination of students will get the prize, but we wouldn't know which (10K, 5K, or 1K) type of scholarship these students will receive. If we know that there will be two of each (from (2)), then we will be able to figure that out.

But yes, it would be great if the experts can chime in.

Thanks!