Answer:
Hence, the probability that the first 3 cars are in car number order is:
[tex]\dfrac{1}{720}[/tex]
Step-by-step explanation:
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
[tex]P(A\bigcap B\bigcap C)=P(A)\times P(B)\times P(C)[/tex]
As, the first car chosen is to be selected among 10 cars.
Hence, the probability is:
[tex]P(A)=\dfrac{1}{10}[/tex]
similarly the second car is to be selected among 9 cars.
Hence,
[tex]P(B)=\dfrac{1}{9}[/tex]
similarly,
[tex]P(C)=\dfrac{1}{8}[/tex]
Hence, the probability that the first 3 cars are in car number order is:
[tex]=\dfrac{1}{10}\times \dfrac{1}{9}\times \dfrac{1}{8}\\\\\\=\dfrac{1}{720}[/tex]
