Lost Cars

Discrete Mathematics Level pending

There is a parking lot with a wall on each end, and 10 side-by-side spaces in between. Ten cars park in these spots: 5 identical blue cars, and 5 different red cars. A blue car owner knows where he is parked if 1) he is next to a red car, or 2) he is on the far left or right (because he knows he is next to the wall). How many different arrangements of red and blue cars can there be in which every blue car knows where he is parked?

(Note: Although the red cars are unique, for the sake of combinations, count them as the same. For example, if there were two different red cars, there would only be 1 combination, RR)

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