Four players compete in a tournament and are ranked from 1 to 4. They then compete in another tournament and are again ranked from 1 to 4. Suppose that their performances in the second tournament are unrelated to their performances in the first tournament, so that the two sets of rankings are independent.
(a) What is the probability that each competitor receives an identical ranking in the two tournaments?
(b) What is the probability that nobody receives the same ranking twice?