A group of 30 students from your school is part of the audience for a TV game show. The total number

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots?

We want the probability a student from your school is chosen out of total students times total ways to choose students from your school:

a) P(5 students being selected):
5/30 * 4/(120 - 30)
5/30 * 4/90
20/2700
Simplifying this fraction, we get:
1/135

b) Total Ways 9 students can be picked from your school:
9/120

Simplifying this fraction, we get:
3/40

Divide a by b:
1/135 / 3/40
40/405

Simplifying, we get:
8/81