Question was too long for the title see description

Question

A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 4 students from your school being selected as contestants out of 10 possible contestant​ spots?

Answer 1

This is an hypergeometric distribution problem. The numbers needed to calculate the answer are big and will require some care even with your calculator,

_nC_r is the binomial coefficient of picking r things from n.

Your probability is ₄₀C₄ * ₉₀C₆ / ₁₃₀C₁₀.

The numbers are marginal for using the binomial to approximate the answer or the normal approximation to the binomial. Since calculators are easily available, I would recommend doing the direct calculation of the binomial coefficients and the division.