Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that exactly one woman left the elevator.
The total number of sets of 4 people is given by C(12, 4) = 495
The numer that contain exactly 1 woman = C(5,3) * C(7,1) = 70
So...the probability is 70 / 495 = 14 / 99
