Suppose that there are 100 applicants for 5 positions at a certain company, and the company is able to narrow the final field to 13 equally qualified candidates. Seven of the finalists are men and 6 are women. Assume that the 5 who are chosen for the positions

are selected at random (not a good way to pick!) from the final group of 13. Calculate the probability that:

a. Three of the five hired are women.

b. None of the males are hired.

c. At least one of those hired is a male.

d. Only one of the women is hired.