Question

The students' council in a school is made up of 9 grade 12 students and 6 grade 11 students. A committee of 5 students is being randomly selected from the council. What is the probability that the committee will have 4 grade 11's and 1 grade 12 student?

Answer 1

`135/3003~~0.045=4.5%`

Explanation:

We will divide the number of ways we can create a committee of 4 grade 11s and 1 grade 12 by the number of ways we could pick a committee from all the students.

4 grade 11s, 1 grade 12

We can choose 4 grade 11s from the population of 6 and we can choose 1 grade 12 from the population of 9. Since these are independent choosings, we'll multiply them.

The combination general formula is

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`:

`C_(6,4)xxC_(9,1)=(6!)/((4!)(2!))xx(9!)/((1!)(8!))=15xx9=135`

No restrictions

The number of ways we can pick 5 people from the total grade 11 and 12 population (of 15 people) is:

`C_(15,5)=(15!)/((5!)(10!))=3003`

Which means that the probability that the council is made up of 4 grade 11s and 1 grade 12 is:

`135/3003~~0.045~~4.5%`