Question

A group of ten women and ten men are in a room. a committee of four is chosen at random. find the probability that the committee consists only of women?

Answer 1

First, we determine the sample space of choosing four members of the committee from 20 persons (both men and women). That is,
                                 20C4 = 4845
Then, we determine the combination of choosing these 4 members only from the group of women. That is,
                              10C4 = 210
The probability is calculated by dividing the second answer by the first answer which will give us an answer of 14/323.