Question

A train has 10 cars numbered 1 through 10. If the cars are coupled randomly, what is the probability that the first3 cars are in car number order?

Answer 1

You would have a 3 to 10 chance that the first 3 cars are in order

Answer 2

`(1)/(720)`

Explanation:

If we arrange the first three cars one by one we get -

Selecting the first car out of ten cars
`= (1)/(10)`

Selecting the second car out of remaining nine cars
`= (1)/(9)`

Selecting the third car out of remaining eight cars
`= (1)/(8)`

So, the probability of selecting three cars back to back without repeating is given by

Probability of Selecting the first car out of ten cars * Probability of Selecting the second car out of remaining nine cars * Probability of Selecting the third car out of remaining eight cars

`= (1)/(10) * (1)/(9)* (1)/(8)\\= (1)/(720)`