Suppose there are 500 applicants for five equivalent positions at a factory and the company is able to narrow the field to 30 equally qualified applicants. Seven of the finalists are minority candidates. Assume that the five who are chosen are selected at random from this final group of 30.

a. In how many different ways can the selection be made?

b. What is the probability that none of the minority candidates is hired?

c. What is the probability that no more than one minority candidate is hired?