Answer:
There are 108900 different committees can be formed
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