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?

18

Step-by-step explanation:

First choose the president. From the 4 people, everyone can be the president except Dan, so there are 3 choices.

Then, choose the treasurer. Neither Bob nor Dan can be the treasurer so there are only 2 choices.

Now choose the secretary. Cyd is the only person who can't take this position, so there are 3 choices.

We are asked by the number of ways of choosing the 3 officers. Using the product rule, this is equal to 3×2×3=18.