A committee consisting of a president, a secretary, and a treasurer, is to be chosen from among four people: Amy, Bob, Charlotte, and Dan. Amy and Bob cannot be president, Charlotte and Dan cannot be secretary. No person can serve in more than one role.

(a) Draw the possibility tree corresponding to the following order of steps: step 1: choose treasurer, step 2: choose president, step 3: choose secretary. Is the number of options in each step independent of the choices made in previous steps? If not, why? If yes, apply the multiplication rule to compute how many different committees are possible.

(b) Draw the possibility tree corresponding to the following order of steps: step 1: choose president, step 2: choose secretary, step 3: choose treasurer. Is the number of options in each step independent of the choices made in previous steps? If not, why? If yes, apply the multiplication rule to compute how many different committees are possible.