<h3><u>
Answer:</u></h3>
Hence, the probability that the first 3 cars are in car number order is:
![\dfrac{1}{720}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B720%7D)
<h3><u>
Step-by-step explanation:</u></h3>
A train has 10 cars numbered 1 through 10.
If the cars are coupled randomly, what is the probability that the first 3 cars are in car number order.
The probability of the three cars is independent and we know that when the events A,B and C are independent then
![P(A\bigcap B\bigcap C)=P(A)\times P(B)\times P(C)](https://tex.z-dn.net/?f=P%28A%5Cbigcap%20B%5Cbigcap%20C%29%3DP%28A%29%5Ctimes%20P%28B%29%5Ctimes%20P%28C%29)
As, the first car chosen is to be selected among 10 cars.
Hence, the probability is:
![P(A)=\dfrac{1}{10}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cdfrac%7B1%7D%7B10%7D)
similarly the second car is to be selected among 9 cars.
Hence,
![P(B)=\dfrac{1}{9}](https://tex.z-dn.net/?f=P%28B%29%3D%5Cdfrac%7B1%7D%7B9%7D)
similarly,
![P(C)=\dfrac{1}{8}](https://tex.z-dn.net/?f=P%28C%29%3D%5Cdfrac%7B1%7D%7B8%7D)
Hence, the probability that the first 3 cars are in car number order is:
![=\dfrac{1}{10}\times \dfrac{1}{9}\times \dfrac{1}{8}\\\\\\=\dfrac{1}{720}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B10%7D%5Ctimes%20%5Cdfrac%7B1%7D%7B9%7D%5Ctimes%20%5Cdfrac%7B1%7D%7B8%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B720%7D)