Suppose there are n people at a party, and the guests have put their coats in a dark coat room. As the guests leave, they grab their coats from the coat room at random (without replacement), since they cannot see. Required:
a. What is the probability that the first two people to leave both get their own coats?
b. What is the probability that every person manages to get his or her own coat?
c. What is the probability that nobody gets his or her own coat?
d. What does the answer to part (c) approach as n rightarrow infinity?
e. What is the expected number of people that get their own coat?