Suppose that a law firm has 16 lawyers and these are to be selected randomly to represent the company at the annual meeting of the Australian Bar Association. How many different combinations of 3 lawyers could be sent to the meeting?

Out of 10 men, there are 4 doctors, 3 teachers and 3 lawyers and out of 8 women, there are 3 doctors, 3 dancers and 2 lawyers. In how many ways can a committee of 5 persons be formed such that , There are 3 doctors and 2 lawyers in the committee?Options7C3 x 5C210C5 x 8C57C5 x 5C510C7 x 8C5

Select four executives from 15 executives to participate in this year's summary meeting. How many choices are there?

Answer the questions below.(If necessary, consult a list of formulas.)(a) From a collection of 51 store customers, 3 are to be chosen to receive a special gift. How many groups of 3 customers are possible?(b) A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

There are twelve students in a group, they want to choose three people at random for the speech contest, how many different three-people groups are possible?

A committee of 5 members is going to be formed from 3 Trainers, Four Professors and 6 Research Associates. How many ways can they be selected, if- in committee, there are 2 Trainers and three Research Associates?