3. A president, treasurer, and secretary, all different, are to be chosen from a club consisting of...

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3. A president, treasurer, and secretary, all different, are to be chosen from a club consisting of 10 people. How many different choices of officers are possible if

(a) there are no restrictions;

(b) A and B will not serve together;

(c) C and D will serve together or not at all;

(d) E must be an officer;

(e) F will serve only if he is president?

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