MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

Answer:There are 97920 ways to formed the committeeStep-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