A board of directors consists of eight men and four women. A four-member search committee is to be chosen at random 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 probability of selecting all four women from a group of 12 people (8 men and 4 women) is calculated using combinations. The number of ways to choose 4 women out of 4 is $C(4,4) = 1$, and the total number of ways to choose any 4 people out of 12 is $C(12,4) = 495$. Thus, the probability is $1/495$.

A Board of Directors Consists of Eight Men and Four