Answer:
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
