a club has 30 members including 3lawers, 4 teachers and 5 doctors. In how many ways can a committee of 8 be formed to contain 1 teacher, 2 lawyers and 2 doctors?

Answer 1

the categories can be considered separately, so working with the specialties first, there would be 3C2 * 4C1 * 5C2 = 3*4*10 = 120 ways to pick them.

Then, with 5 slots already filled, that leaves only 25 left to choose the other 3 members, or 25C3 = 2300

So, that makes 120 * 2300 = 276,000 ways to form the committee.