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.FindA) 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?