Question

There are 10 students in a class: 7 boys and 3 girls. if the teacher picks a group of 5 at random, what is the probability that everyone in the group is a girl?

Answer 1

Answer:

1/12 ≈ 8.33%

Step-by-step explanation:

If there's only 3 girls, then there's no way that a group of 5 can be all girls.  I assume you mean that there are 7 girls and 3 boys?

The number of ways to choose 5 students from 10 is ₁₀C₅.  This is the total number of combinations possible.

The number of ways to choose 5 students from 7 girls is ₇C₅.

So the probability is:

P = ₇C₅ / ₁₀C₅

P = 21 / 252

P = 1 / 12

P ≈ 8.33%