In how many ways can 12 different cars be displayed along the circumference of a parking area?

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Nine cars are parked in a row. Four of the cars are painted red and five are painted blue. In how many ways can the cars be parked so that there are never two red cars next to each other?

I think I know how to solve this but I am not sure.

First arranging the blue cars in line and specifying where the red ones could be parked.

$$\color{red}X\color{blue}B\color{red}X\color{blue}B\color{red}X\color{blue}B\color{red}X\color{blue}B\color{red}X\color{blue}B\color{red}X$$

Where $\color{blue}B$ stands for a parked blue car and $\color{red}X$ for a potential red car parking spot. So we have 6 $X's$ (red cars) and 5 $B's$ (blue cars). Note all cars are considered to be the same.

Then the answer is $C(6,4) = 15$?

You can put this solution on YOUR website!

Hi,

In how many ways can