1. At a party n men take off their hats. The hats are then mixed up and each man randomly selects one. We say that a match occurs if a man selects his own hat. What is the probability of no matches? What is the probability of exactly k matches?

2. (The Ballot Problem) In an election, candidate A receives n votes, and candidate B receivesm votes where n > m. Assuming that all orderings are equally likely, show that the probability that A is always ahead in the count of votes is (n - m)/(n + m).