Five hats are randomly distributed to the five people who own them. What is the probability that all the people receive the correct hat?
Alternate Problem 4
Three people leave identical coats in a checkroom. When the people check out, the three coats are distributed at random to the people. What is the probability that none of the people receives the correct coat?
Extension Problem 4
Two people are playing a game in which a coin is tossed 11 times. The first player gets a point for a toss of heads. The other player gets a point for a toss of tails. Whoever gets 6 points first wins. Suppose that so far, the first player has 2 points, and the second player has 4 points. What is the probability that the first player wins the game?