confused as to what formula i should use

Question

A committee of six people is formed to investigate connections between business and the education system. It consists of people chosen from 5 students, 8 teachers, 5 Principles, 10 parents, 4 professors, and 6 business people. If the members are chosen at random, what is the probability that there is one person from each group on the committee

Answer 1

The number of ways of choosing one person from each group is ₅C₁×₈C₁×₅C₁×₁₀C₁×₄C₁× ₆C₁=48000

The number of ways of choosing six people from 38 people is ₃₈C₆=2760681

The probability in question is the ratio 48000/2760681