A certain roller coaster has 7 cars, and a passenger is equally likely to ride in any 1 of the 7 ...
A certain roller coaster has 7 cars, and a passenger is equally likely to ride in any 1 of the 7 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 7 times, what is the probability that the passenger will ride in each of the 7 cars?
Answer/Solution
720/16807
Steps/Work
If he is to ride 6 times and since he can choose any of the 6 cars each time, total number of ways is
= 7 * 7 * 7 * 7 * 7 * 7
= 117649
Now the number of ways if he is to choose a different car each time is
= 7 * 6 * 5 * 4 * 3 * 2 * 1
= 5040
So the probability is
= 5040/117649 = 720/16807
Answer : D
= 7 * 7 * 7 * 7 * 7 * 7
= 117649
Now the number of ways if he is to choose a different car each time is
= 7 * 6 * 5 * 4 * 3 * 2 * 1
= 5040
So the probability is
= 5040/117649 = 720/16807
Answer : D