The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28
Step-by-step explanation:
School students = 40
Total people = 130
Total contestant spot = 9
Probability of 3 contestant from school = ?
The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃
The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆
The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆
The total number of possible 9 contestants from the audience = ¹³⁰C₉
Probability of the group of contestants having 3 students =
Solving the equation further we get:
Probability of the group of contestants having 3 students = 0.28