Probability of All Women Search Committee

C

4/12*3/11*2/10*1/9 = 1/495

To calculate the probability that all four members of the search committee will be women, we need to determine the total number of possible search committees and the number of search committees consisting of only women.

Total Number of Search Committees: The search committee consists of four members chosen from a total of twelve directors (eight men and four women). We can calculate the total number of search committees using the combination formula (nCr):

Total Committees = 12C4 = 12! / (4! * (12 - 4)!) = 12! / (4! * 8!) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1) = 495

Number of Committees with Only Women: Since we want all four members of the search committee to be women, we need to select four women from the available four women. We can calculate the number of search committees with only women using the combination formula (nCr):

Committees with Only Women = 4C4 = 4! / (4! * (4 - 4)!) = 1

Probability Calculation: To find the probability, we divide the number of committees with only women by the total number of search committees:

Probability = Committees with Only Women / Total Committees = 1 / 495

Therefore, the correct answer is C. 1/495 or approximately 0.002.