Question

How many different committees can be formed from 12men and 12 women if the committee consists of 3 men and 4 women?

Answer 1

Answer:

There are 108900 different committees can be formed

Step-by-step explanation:

* Lets explain the combination

- We can solve this problem using the combination

- Combination is the number of ways in which some objects can be

 chosen from a set of objects

-To calculate combinations, we will use the formula nCr = n!/r! × (n - r)!

 where n represents the total number of items, and r represents the

 number of items being chosen at a time

- The value of n! is n × (n - 1) × (n - 2) × (n - 3) × ............ × 1

* Lets solve the problem

- There are 12 men and 12 women

- We need to form a committee consists of 3 men and 4 women

- Lets find nCr for the men and nCr for the women and multiply the

 both answers

∵ nCr = n!/r! × (n - r)!

∵ There are 12 men we want to chose 3 of them

∴ n = 12 and r = 3

∴ nCr = 12C3

∵ 12C3 = 12!/[3!(12 - 3)!] = 220

* There are 220 ways to chose 3 men from 12

∵ There are 12 women we want to chose 4 of them

∴ n = 12 and r = 4

∴ nCr = 12C4

∵ 12C4 = 12!/[4!(12 - 4)!] = 495

* There are 495 ways to chose 4 women from 12

∴ The number of ways to form different committee of 3 men and 4

   women = 220 × 495 = 108900

* There are 108900 different committees can be formed