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.

In order to figure out how to distribute these scholarships, we need to know how many of them there are, and how many of each kind.
If we call the 10K ones A, the 5K ones B, and the 1K ones C, then we have a number of ways this can go.

We might have A, A, A, A, B, and C to distribute, or we might have A, A, B, B, C, and C to distribute. (or obviously many other possible allocations) These will result in different answers.

Thus, we need both statements.

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