Question

A small business employs 6 women and 4 men. The manager randomly selects 3 of them to be on a team. What is the probability that all 3 are women?

Answer 1

Total of 10 persons, out of which 6 are women.
So
probability of choosing the first woman = 6/10
probability of choosing the second woman = 5/9
probability of choosing the third woman = 4/8

Since we want all 3 steps to be a success, we need to have success in each of the steps, and the overall probability is given by the multiplication rule:
P(all 3 are women)=6/10*5/9*4/8=120/720=1/6