200 people apply for 3 jobs. 60 are women. If 3 persons are selected randomly, what is probability 2 are women

Answer 1

I will assume that the question means what is the probability that exactly 2 are women are chosen (as opposed to either two or three are women).

For the first person selected at random, there is a probability of 60/200 that it is a woman selected. That's the same as 3/10.

For the second person selected at random, there is a probability of 59/199 that it is a woman selected.

For the third person selected at random, there is a probability of 140/198 that it is a man selected which is the same as 70/99

So the probability that all three events occur is 3/10 • 59/199 • 70/99 = 12390/197010 = 413/6567