Question: Suppose that n cars are in the line to enter a parking lot that has n spaces, side to side in a straight line. The first car can choose any space and every one of the other cars when parking have to chose a juxtaposed position of a car that is already parked. How many are the possible ways that those n cars can occupy those n spaces?
So, since the first car can choose any of the n spaces to park, if it chooses the first place, the other car is going to have only one possibility which is to the right.But, if the car chooses any place in the middle, all the others are going to have two possibilities. So, maybe we are going to have 2^(n-1) possible ways of organizing this parking lot?