In how many ways can a club with 17 members elect a president, vice president, a

Question

In how many ways can a club with 17 members elect a president, vice president, and secretary (assuming no person can fill more than one office) for each situation described?

(a) There are no restrictions.

(b) Susan has removed herself from consideration for president due to a busy schedule, but she is willing to serve in either of the other offices.

(c) Sam has indicated that he will serve as president only if Mary is named as the vice president.

(d) The club’s bylaws require that last year’s vice president becomes this year’s president.

I'm just lost.

Explanation / Answer

a) = 17C3 x 3!= 4080 b) = 17C3x3! - 16C2x2! = 3840 c) = 16C3x3! + 15C1 + 2x16C2x2! = 3855 d) = 16C2 x2!= 240

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