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Question about Discrete Structure: Ten students are competing for scholarships. Suppose that no student can win...

Question about Discrete Structure:

Ten students are competing for scholarships. Suppose that no student can win more than one scholarship. (Each part below is independent of the others.)

(a) Suppose that there are three scholarships which are worth $1000, $2000, and $5000. In how many different ways can the scholarships be distributed?

(b) Suppose that there are three scholarships worth $2000 each. In how many different ways can the scholarships be distributed?

(c) Suppose that there are two scholarships worth $5000 and three worth $2000. In how many different ways can the scholarships be distributed?

(d) Suppose that the group of ten students consists of six freshmen and four sophomores. In how many different ways can four equal scholarships be distributed if at least two of the scholarships should be awarded to freshmen?

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