Probability Question

Question

Twenty elk live in a forest, and 7 were tagged and released. Some time later, 5 elk were randomly caught. Assume all 20 elk were equally likely to be caught. What is the probability that exactly 2 of these 5 elk caught were previously tagged? Do NOT round.

Answer 1

This is called the hypergeometric problem Of the 5 that you choose from 20, 2 must be from the tagged(7) and 3 must be chosen from the untagged (13)

The solution is ₇C₂ * ₁₃C₃ / ₂₀C₅ where _nC_k = n!/(k!(n-k)!)