The resumes of 2 male applicants for a Ph. D. position in the college of engineering are placed in the same file as the resumes of 2 female applicants. Two positions become available and the first is filled by selecting 1 of the 4 applicants at random. The second position is then filled by selecting at random one of the remaining 3 applicants. Using the notation M1F1, for example, to denote the simple event that the first position is filled by the first male applicant and the second position is then filled by the first female applicant, a. (1 pts) List the elements of a sample space S; b. (1 pts) List the elements of S corresponding to event A that the first position is filled by a female applicant; c. (1 pts) List the elements of S corresponding to event B that exactly one of the two positions was filled by a female applicant; d. (1 pts) List the elements of S corresponding to event C that neither position was filled by a female applicant; e. (1 pts) List the elements of S corresponding to event D that the first position is filled by a female applicant and the second position is not filled by a female; f. (1 pts) List the elements of S corresponding to event E that at least one of the positions is filled by a female; g. (2 pts) List the elements of S corresponding to the event ′ ∩ ; h. (2 pts) List the elements of S corresponding to the event ∩ ′; i. (1 pts) Construct a Venn diagram to illustrate C and A are mutually exclusive; j. (2 pts) Construct a Venn diagram to illustrate ′ ∩ k. (2 pts) Construct a Venn diagram to illustrate ( ∪ ′)