Alice, Ben, Connie, Doug, Ed, Fred, Grace, Hugo, Icabod

| August 30, 2017

Question
Q:Alice, Ben, Connie, Doug, Ed, Fred, Grace, Hugo, Icabod, Jed and Ken are in a club. They will elect a President, Vice President and Treasurer.

Find

A) If Grace can not be President, Fred can not be Vice President and Ken can not be Treasurer, how many ways can they elect a President, Vice President and Treasurer?

B) If Grace says she will only be an officer if Jed is an officer, how many ways can they elect a President, Vice President and Treasurer?

C) If Alice says she will not be an officer if Ben is an officer, how many ways can they elect a President, Vice President and Treasurer?

D) If Doug and Ed must both be officers but Connie can not be, how many ways can they elect a President, Vice President and Treasurer?

E) If Ed must be an officer, and Doug will not serve if Connie is an officer, how many ways can they elect a President, Vice President and Treasurer?

F) If Jed will not be an officer if a girl is President (Alice, Connie and Grace are girls), how many ways can they elect a President, Vice President and Treasurer?

G) If Ken will only be an officer if a girl is President, how many ways can they elect a President, Vice President and Treasurer?

H) If the officers are all of the same gender, how many ways can they elect a President, Vice President and Treasurer?

I) If the Vice President and Treasurer are a different gender than the President, how many ways can they elect a President, Vice President and Treasurer?

J) If they must have at least one officer from each gender, how many ways can they elect a President, Vice President and Treasurer?

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