Question

We have three cars with four people in each car. If the car owner must occupy their own car, how many arrangements of the people are possible?

Answer 1

84

Explanation:

The number of combinations of `n` people taken `p` at a time is given by `""_nC_p = (n!)/(p!(n-p)!`

In this example, there are 3 cars each with 4 people in each.
The people in each car are: 1 owner + 3 passengers

The owner is fixed per car so the number of arrangements (combinations) of the remaining 9 people is `""_9C_3`

`=(9!)/(3!*6!)`

`=(9xx8xx7)/(3xx2xx1)=84`