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

Answer 1

To calculate the total number of ways the committee can be formed, we need to consider the options for each profession separately.

For teachers:
From 4 teachers, we need to select 3, so the number of ways to select 3 teachers from 4 is given by the combination formula:
C(4, 3) = 4! / [3!(4-3)!] = 4

For doctors:
From 5 doctors, we need to select 3, so the number of ways to select 3 doctors from 5 is:
C(5, 3) = 5! / [3!(5-3)!] = 10

For lawyers:
From 6 lawyers, we need to select 3, so the number of ways to select 3 lawyers from 6 is:
C(6, 3) = 6! / [3!(6-3)!] = 20

Since the selections are independent of each other, we need to multiply the number of ways each profession can be selected:
Total number of ways = 4 * 10 * 20 = 800

Therefore, there are 800 ways to form the committee with 3 members from each profession.