A roller coaster has 3 cars and a passenger is equally likely to ride in any 1 of the 3 cars each time that a passenger rides the roller coaster. If he rides 3 times, what is the probability the he will ride in each of the 3 cars?
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I am only guessing this approach. This problem is very much like saying you are flipping three coins, 3 times, what is the probability of getting a heads on each coin only in each flip? First flip only first coin gives heads, second flip only second coin gives heads and third flip only third coin gives heads.
The probability of taking one specific seat among the 3 seats is 1/3, and that of not taking it is 2/3. So you have a bernoulli's trials when 3 times, he might take that seat or not. This is probability with just one seat, with 3 seats, multiply with 3 in the end. The answer must be 3C3(1/3)^3(2/3)^0(3)??
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