A class has six girls and five boys. If the teacher randomly picks six students. What is the probability that she will pick exactly 3 boys?

Answer 1

She can choose the students in 11 C 6 ways.

If she picks 3 boys and 3 girls the boys can be picked in 5 C 3 ways, and the girls in 6 C 3 ways

So by the counting principle this can be done in 5 C 3 x 6 C 3 ways

So probability is (5 C 3) x (6 C 3) / (11 C 6)