2024 NYJC P2 Q6

A carpark has a row of \({10}\) parking lots. On one day the carpark has \({9}\) cars of different makes and \({1}\) empty lot. Of the \({9}\) cars, \({2}\) are blue, \({2}\) are red and the remaining \({5}\) are of other distinct colours.

1. Find the number of different arrangements of the cars in the carpark.[1]
2. Find the number of different arrangements that can be made with both the blue cars next to each other and both the red cars next to each other.[2]
3. Find the number of different arrangements that can be made with no two adjacent cars the same colour.[3]