Question

A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many committees can be formed if no person can serve on more than one committee?

Answer 1

1,260

Explanation:

`\implies C(9,4)*C(5,3)*C(2,2)`

`\implies 9!/4!(9-4)!*5!/3!(5-3)!*2!/2!(2-2)!`

`\implies 9!/4!5!*5/3!2! *2!0!`

`\implies (9 * 8 * 7 * 6 / 4 * 3 * 2 * 1) * (5 * 4 / 2 * 1) * 1`

`\implies 1260`

Therefore, 1,260 committees can be formed.