Three officers - - president, treasurer, and secretary - - are to be chosen from among four people: Ann, Bob, Cyd, and Dan. Bob is not qualified to be treasurer. Cyd's other commitments make it impossible for her to be secretary. Dan is irresponsible with money (cannot be treasurer) and might be corrupted by power (cannot be president). How many ways can the officers be chosen?

13

Step-by-step explanation:

Given that Three officers - - president, treasurer, and secretary - - are to be chosen from among four people: Ann, Bob, Cyd, and Dan.

Ann can take any position, but Bob cannot be a treasurer. Cyd can only be a secretary and Dan cannot be treasure nor manager.

So we have options as

Manager - - Ann, Bob, Cyd

Treasurer - Ann, Dan, cyd

Secretary - - Ann, Dan, Bob

If same person cannot take more than one position, we can have

either (Ann, Dan, Bob) or (Ann, Cyd, Bob) Or (Ann, Cyd, Dan) or (Bob, Dan, Ann) and so on.

i. e. Manager can be selected in 3 ways.

If Manager is Ann, other two can be done in 3 ways

If Bob is Manager, then other two posts can be done in 3 ways

Similarly if Cyd is Manager, then other two can be selected in

7 ways

total ways = 3+3+7 = 13