Roller coaster

[toqueerahmed]

A certain roller coster has 3 cars and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coster. if a certain passenger is to ride the roller coster 3 times, what is the probability that the passenger will ride in each of the 3 cars.

a. 0
b. 1/9
c. 2/9
d. 1/3
e. 1

Can please someone explain the thought process for the answer?

source: GMAT prep

[rkkarthik]

1: The rider can sit in one of the three cars. I.e., 3! ways

2: 3! = 3 * 2* 1 = 6

3: The different ways the rider can choose to sit would be
3 * 3 * 3 = 27

4: Explaining #3:
- The first time he can pick one of the three available cars
- The second time he can pick one of the three available cars
- The Third time he can pick one of the three available cars
Note: No mention of the crowd or other factors;

5: Probability formula :

Number of intended results (AKA Desired outcomes)
--------------------------------------------------------
Number of total options

6: 6 / 27 = 2/9 = Answer Choice 'C'

Good luck
Karthik