Suppose that an employer plans to hire six people from a group of nine equally qualified people, of whom two are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that all two minority candidates are hired? Round your answer to six decimal places.

Question

Suppose that an employer plans to hire six people from a group of nine equally qualified people, of whom two are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that all two minority candidates are hired? Round your answer to six decimal places. ​

Quizplus · Accepted Answer

The total number of ways to select six people from nine is $\binom{9}{6}=84$. The number of ways to select all two minority candidates and any four of the remaining seven candidates is $\binom{2}{2} 	imes \binom{7}{4}=21$. So the probability that all two minority candidates are hired is $\dfrac{21}{84}=\boxed{0.250000}$.

Suppose That an Employer Plans to Hire Six People from a Group