A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?
A)1/120 or 0.00083
B)1/16 or 0.0625
C)1/8 or 0.125
D)1/495 or 0.002

Question

Quizplus · Accepted Answer

The total number of ways to choose a 4-member search committee from twelve directors is:

12C4 = (12!)/(4!8!) = 495

The number of ways to choose all four women from the four available women is:

4C4 = 1

The number of ways to choose zero men from the eight available men is:

8C0 = 1

Thus, the probability of choosing all four women is:

(1)(1)/(495) = 1/495

Therefore, the best choice is D.

A Board of Directors Consists of Eight Men and Four