Solved: The resumes of two male applicants for a college

Chapter 3, Problem 2.11

(choose chapter or problem)

The resumes of two male applicants for a college teaching position in chemistry are placed in the same le as the resumes of two female applicants. Two positions become available, and the rst, at the rank of assistant professor, is lled by selecting one of the four applicants at random. The second position, at the rank of instructor, is then lled by selecting at random one of the remaining three applicants. Using the notation M2F1, for example, to denote the simple event that the rst position is lled by the second male applicant and the second position is then lled by the rst 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 lled by a male applicant; (c) list the elements of S corresponding to event B that exactly one of the two positions is lled by a male applicant; (d) list the elements of S corresponding to event C that neither position is lled by a male applicant; (e) list the elements of S corresponding to the event AB; (f) list the elements of S corresponding to the event AC; (g) construct a Venn diagram to illustrate the intersections and unions of the events A, B, and C.