Six men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that all the women will be interviewed first.Your simulation should use at least 10 runs.
A) $\frac { 1 } { 56 }$
B) $\frac { 1 } { 84 }$
C) $\frac { 1 } { 14 }$
D) $\frac { 1 } { 28 }$
E) $\frac { 2 } { 3 }$

Question

Quizplus · Accepted Answer

The probability that all women will be interviewed first is calculated by considering the total ways to arrange the women (which is always 1 way since all must go first) over the total ways to arrange all 9 people. The total ways to arrange 9 people is 9!, and since the order of the 3 women doesn't matter when they are all interviewed first, we divide by the ways to arrange the 6 men, which is 6!. Therefore, the probability is 1/(9!/(3!6!)) = 1/84.

Six Men and Three Women Are Waiting to Be Interviewed 156\frac { 1 } { 56 }561​

Six Men and Three Women Are Waiting to Be Interviewed $\frac { 1 } { 56 }$