The qualified applicant pool for three management trainee positions consists of seven men and six women. If the applicants are equally qualified and the trainee positions are selected by drawing the names at random so that all groups of three are equally likely, what is the probability that the trainee class will consist entirely of men? Round your answer to the nearest thousandth.
A)0.007
B)0.073
C)0.122
D)0.003
E)none of these choices

Question

Quizplus · Accepted Answer

There are a total of $\binom{13}{3} = 286$ ways to choose a group of three out of thirteen people. There are $\binom{7}{3} = 35$ ways to choose a group of three men out of seven men. So the probability that a randomly chosen group of three people consists of all men is $\dfrac{35}{286} \approx \boxed{0.122}$.

The Qualified Applicant Pool for Three Management Trainee Positions Consists