Suppose a class has forty students, with twenty men and twenty women, including two women, Alice and Beth, and two men, Chuck and Dan. All forty students have been randomly assigned into ten study groups of four students each.

a) What is the probability that Alice and Beth are both assigned to the same group?

b) If Alice's group has exactly two women, what is the probability that Alice and Beth are both assigned to the group?

c) What is the probability that Alice is in a group with Chuck and Beth is in a group with Dan? (if the two pairs are in groups together, they can be in separate groups or all in the same group)

d) Given that Alice is in a group with Chuck and Beth is in a group with Dan, what is the probability that all four of them are in the same group?

e) What is the probability that all women are assigned to groups that include only women?

f) What is the probability that at least one group includes three or more women?