4.137 Orchestra Politics The board of directors of a major symphony orchestra has voted to create a players' committee for the purpose of handling employee complaints. The council will consist of the president and vice-president of the symphony board and two orchestra representatives. The two orchestra representatives will be randomly selected from a list of six volunteers, consisting of four men and two women.

a. Find the probability distribution for X, the number of women chosen to be orchestra representatives.

b. Find the mean and variance for the random variable X.

c. What is the probability that both orchestra represen- tatives will be women?