There are 6 applicants for the Director of Marketing. The applicants are interviewed independently by each member of the three-person search committee and ranked from 1 to 6. A candidate will be hired if he or she is ranked first by at least two of the three interviewers.

a. Find the probability that a candidate will be accepted if the members of the committee really have no ability at all to judge the candidates and just rank the candidates randomly.

b. What is the probability if only 3 applicants are shortlisted?