Answer:
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