A student's work to simplify a radical is shown below. Select the statement which best applies to the sample mathematical work.
54 =27 2
27 2 = 332
Thus, 54 = 3/2
A. The equality 54 = 27.2 is incorrect or invalid.
B. Removing the 27 from under the radical in the second step is incorrect or invalid.
C. The work shown above is correct, however 3/2 may be simplified further.
D. The work shown above is correct, and 32 may not be simplified further.

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three 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 one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.