Question

Three students are selected at random from a class consisting of 5 freshman, 3 sophomores, and 2 juniors. Find the probability that 2 freshman and 1 junior are selected given that at least 1 freshman is selected.

Answer 1

There are 10 students and 3 are selected. When 1 freshmen is selected, it leaves 9 students and 2 slots. There are 72 different events because there are 9 students for the first one of those two and 8 for the other. You then have to find how many of them have 1 freshmen and 1 junior. There are 12 events were a freshmen is chosen after a junior and 12 were they are chosen before a junior. (3x4). this means that 24/72 events meat the criteria so their is a 1/3 or 33.3% chance.