The resumes of 2 male applicants for a college teaching position in chemistry are placed in the same file as the resumes of 2 female applicants. Two positions become available and the first, at the rank of assistant professor, is filled by selecting 1 of the 4 applicants at random. The second position, at the rank of instructor, is then filled by selecting at random one of the remaining 3 applicants. Using the notation M2F1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant,
(a) List the elements of a sample space S;
(b) List the elements of S corresponding to event A that the position of assistant professor is filled by a male applicant;
(c) List the elements of S corresponding to event B that exactly 1 of the 2 positions was filled by a male applicant;
(d) List the elements of S corresponding to event C that neither position was filled by a male applicant;
(e) List the elements of S corresponding to the event A ∩ 5 ;
(f) List the elements of S corresponding to the event A DC:
(g) Construct a Venn diagram to illustrate the intersections and unions of the events A, B, and C.