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

There are 97920 ways to formed the committee

Step-by-step explanation:

* Lets solve explain the combination

- combination is a collection of the objects where the order doesn't

matter

- Combinations is nCr, where n is the total number and r is the number

of the choices

# Example: chose a group of three students from the group of 10

students n = 10 and r = 3, then 10C3 is 120

* Lets solve the problem

- The club has 30 members

- There are 3 lawyers, 4 teachers, 5 doctors in the group

- We want to formed a committee of 8 contains 1 teacher, 2 lawyers,

2 doctors

∵ There are 4 teachers, we want to chose 1 of them

∴ 4C1 = 4

∵ There are 3 lawyers, we want to chose 2 of them

∴ 3C2 = 3

∵ There are 5 doctors, we want to chose 2 of them

∴ 5C2 = 10

- To find how many ways multiply 4C1 by 3C2 by 5C2

∵ 4C1 * 3C2 * 5C2 = 4 * 3 * 10 = 120

∵ The total numbers of the teachers, the lawyers and the doctors is

4 + 3 + 5 = 12 members from the 30 members

∴ There are 120 ways to chose 5 members from 12 members

∵ The committee has 8 members

∴ We want to chose another 3 from the rest of the members

∵ The rest of the members = 30 - 12 = 18

∴ We must to find 18C3

∵ 18C3 = 816

- To find the total ways of the 8 members multiply the ways of the 5

members and the 3 members

∴ The total number of ways = 120 * 816 = 97920

∴ There are 97920 ways to formed the committee