1. An urn contains five red, five black, and five white balls. If three balls are chosen without replacement at random, what is the probability that they are of exactly two different colors?
2. (A Problem of Tom Sellke). Suppose that cards are picked at random from a full deck of 52 cards.
(a) What is the probability that exactly one jack, one queen, and one king have been picked from the deck when the first ace turns up?
(b) What is the probability that exactly two jacks, two queens, and two kings have been picked from the deck when the second ace turns up?
3. (Coincidence, Again). Four men throw their watches into the sea, and the sea brings back to each man at random one watch. What is the probability that exactly one man gets his own watch back?