Problem
The resum´es of two male applicants for a collegeteaching position in chemistry are placed in the samefile as the resum´es of two female applicants. Two positionsbecome available, and the first, at the rank ofassistant professor, is filled by selecting one of the fourapplicants at random. The second position, at the rankof instructor, is then filled by selecting at random oneof the remaining three applicants. Using the notationM2F1, for example, to denote the simple event thatthe first position is filled by the second male applicantand the second position is then filled by the first femaleapplicant,
(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 maleapplicant;
(c) list the elements of S corresponding to event B thatexactly one of the two positions is filled by a maleapplicant;(d) list the elements of S corresponding to event C thatneither position is filled by a male applicant;
(e) list the elements of S corresponding to the eventA n B;
(f) list the elements of S corresponding to the eventA ? C;
(g) construct a Venn diagram to illustrate the intersectionsand unions of the events A, B, and C.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.