1 Throwing Frisbees

Bob and his n 1 friends stand in a circle and play the following game: Bob throws a frisbee to one of the other people in the circle randomly, with each person being equally likely, and thereafter, the person holding the frisbee throws it to someone else in the circle, again uniformly at random. The game ends when someone throws the frisbee back to Bob.

(a) What is the expected number of times the frisbee is thrown through the course of the game?

(b) What is the expected number of people that never got the frisbee during the game?