There are 10 students in a class: 6 boys and 4 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?
My counting and probability is not very good but I'll try. I think this is how to do the problem:
We look at where the teacher chooses all girls in the group. It's a group of 3 and there are 4 girls so there are 4C3=4 ways to choose 3 girls(a group). Then we look at the total number of groups the teacher can choose which is 10C3=120. Therefore the probability everyone in the group is a girl is 4/120=1/30.