Question

Suppose that a class contains 15 boys and 30 girls and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.

Answer 1

There are

N = C(45,10) = 45!/(10!(45-10)!) = 3190187286

ways to choose 10 students from 45 students. Among them, there are

M = C(15, 3) = 15!/(3!(15-3)!) = 455

ways to choose 3 boys from 15 ones. Therefore, the probability that exactly 3 boys will be selected is

P = M/N = 455/3190187286 ≈ 0.0000001426.