There are 7 students in a class: 5 boys and 2 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?

Answer 1

The probability of picking a boy on the first pick is 5/7. Now there are only 4 boys left and 6 students, so the probability of picking a boy on the second pick is 4/6. On pick three, there are 3 boys left and only 5 students, so the probability of picking a boy on the third pick is 3/5. The probability of picking 3 boys then is:

P(3 boys) = (5/7)·(4/6)·(3/5) = ______?