Problem of the Week 4

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?