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

Answer:

$\frac{1}{720}$

Step-by-step explanation:

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

Selecting the first car out of ten cars $= \frac{1}{10}$

Selecting the second car out of remaining nine cars $= \frac{1}{9}$

Selecting the third car out of remaining eight cars $= \frac{1}{8}$

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

$= \frac{1}{10} * \frac{1}{9}* \frac{1}{8}\\= \frac{1}{720}$