Question

There are 15 stations on a railway line. How many tickets of different stations should be printed so that a passenger can buy a ticket from any station from another?

Answer 1

Hint: We here have been given 15 stations in a railway line and we need to find the total number of different tickets so that a passenger can travel to any other from all the stations. For this, the number of tickets each station should have will be equal to one less than the total number of stations and since there are a total of 15 stations, the total number of different tickets should be equal to the product of 15 and one less than the total number of stations. Finding this product, we will get the required answer.

Complete step by step answer:
Now, we have been given 15 stations in a railway line and we need to find the total number of different tickets so that a passenger can travel to any other station from any one station.
Now, since there are a total of 15 stations, each station should contain a ticket of all the other stations. Hence, each station should have a ticket for $15-1=14$ stations.
Thus, each station should have a total of 14 tickets.
Now, since there are a total of 15 stations, the total number of tickets will be given as:
$15\times 14$
Now, solving this, we get:
$\begin{align}
  & 15\times 14 \\
 & \therefore 210 \\
\end{align}$
Thus, each station should have a total of 210 tickets.

So, the correct answer is “210”.

Note: Here, we have considered the tickets to be different even when the destination is the same. This is because the starting point in every journey is different and two tickets are only the same if both the starting point and the destination of the journey is the same. If any one of them is different, then the tickets are also different.