Probability word problem

Question

You need to select a President, Vice President, and Treasurer from a class of 25. If 17 of the students are boys, what is the probability that all three students on the committee are girls? Leave your answer as a fraction . No need to reduce the fraction.

Answer 1

Just count it out. There are three slots and you want them all to be girls. For any slot the probability of picking a girl is the number of girls divided by the number of people. With no replacement, the next slot will have one fewer girl and one fewer person to choose from.

P(3G) = (8/25)(7/24)(6/23)