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
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.