Beginning counting and Probability Marathon

Hey, I'm starting a c+p marathon.

There is a board of 15 members that wants to choose a president, vice-president, and treasurer. How many possible outcomes are there in each of the following:
a) each member can only hold one office

b) each member can hold up to three offices

c) Alice will only hold an office if Bob is holding an office

(My brain is blank so i may have done some stupid things ok?)

a. thats 15 x 14 x 13 or 2730

b. thats 15 x 15 x 15 or 3375

b. case one Alice and Bob are not in office: 13 x 12 x 11 = 1716
case two Alice and bob are in office: 1 x 1 x 13 x 3 = 39
answer; 1755

I may have TOTALLY FAILED this one so please correct me when you see an error.

Problem 2:
Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle?