Probability

First time he rides the roller coaster the probability of him picking a cart he hasn't ridden before is 1, since it's the first time he rides it.
Second time he rides the roller coaster the probability of him picking a cart he hasn't ridden before is 2/3, since he's already ridden one of the three carts.
Third time he rides the roller coaster the probability of him picking a cart he hasn't ridden before is 1/3, since he's already ridden two of the carts.

So my answer will be 1*1/3*2/3 =2/9.

Thanks Dana. It makes sense.

I had difficulty because I translated the problem: there are 3 balls in a bag, each in different color. Pick up any one ball from the bag without looking into it, then put it back. What is the probability of picking 3 times and each time it's a different color?

I think it's the same as the original question (taking different car each time for 3 times). So my calculation is 1x1/3x1/3=1/9. What is the problem in my calculation or translation?