Question

I have a car dealership employing 4 mechanics. I received 20 cars to repair today. How

many possible ways can I assign the cars to the mechanics?

Answer 1

We are given that car dealership employed 4 mechanics. and 20 cars came there.

That means each employee should handle
`(20)/(4) = 5 cars`

Which means we need to choose 5 cars from 20 cars first . For that we need to use combinations since order in which car is given to mechanic does not matter.

Hence number of ways =
`20_{C_(5) }` =
`(20! )/(15! * 5!)` = 15504 ways of allocating.