Suppose a class has seventy-five students, with twenty-five men and fifty women. All the students have been randomly assigned into twenty-five study groups of three students each. a) Find the probabilities for the events ! = "the first group has three women", and !" = "the first group has three women and the second group has three women".

b) Consider the number of groups that have three women, . Find its expected value and variance.

c) Use Chebyshev to find an upper bound for { 10}.

d) Use the Central Limit Theorem to approximate { 10}.

e) Each woman in the groups with three women wins a prize independently with probability 0.4. Find the expected value and variance of the total number of prizes won.