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A group of college students contains 7 seniors and 8 juniors. a) In how many ways...

A group of college students contains 7 seniors and 8 juniors.

a) In how many ways can 3 individuals from this group be chosen for a committee?

b) In how many ways can a president, vice president, and secretary be chosen from this group?

c) Suppose instead, there are n seniors and m juniors, for some nonnegative integers n and m.

c-1) In how many ways can k individuals from this group be chosen for a committee, for nonnegative integer k?

c-2) In how many ways can a president, vice president, and secretary be chosen from this group?

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