a committee of 9 peoples is to be form from 4 teachers, 5 doctors and 6 lawyers. if 3 members of each professor are to serve in the committee. how many ways can be selected

Answer 1

To form a committee of 9 people with 3 members from each profession (teachers, doctors, lawyers), we can calculate the number of ways for each profession separately and then multiply the results together.

First, calculate the number of ways to choose 3 teachers from 4:
4 choose 3 = 4! / (3!(4-3)!) = 4 ways

Next, calculate the number of ways to choose 3 doctors from 5:
5 choose 3 = 5! / (3!(5-3)!) = 10 ways

Finally, calculate the number of ways to choose 3 lawyers from 6:
6 choose 3 = 6! / (3!(6-3)!) = 20 ways

Multiply the results together to find the total number of ways to form the committee:
4 ways x 10 ways x 20 ways = 800 ways

Therefore, there are 800 ways to select a committee of 9 people with 3 members from each profession.