Question

There are 9 students in a class: 7 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?

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Answer 1

I think the teacher would probably pick two boys and one girl

Answer 2

Explanation:

There are 9C3 total ways of picking 3 people from 9 where order does not matter.

To pick 3 boys from 6, you must do 6C3

When you do both of these you divide the smaller by the larger.

9C3 = 84

6C3 = 20

So the probability that you want is

20/84 = 0.238

If you are uncertain where the 84 comes from, it is calculated like this

9*8*7*6! The 6!s cancel out and you are left with

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6! * (9 -6)!

9C3 = 9*8*7/3!

9C3 = 3 * 4 * 7 = 84

6C3 is done exactly the same way.