Question

On Railways there are 15 stations.The number of tickets required in order that it may be possible for a passenger to book from every station 2 every other is what?

Answer 1

The question says the number of ways in which we can travel from every station to every other station. So say the first two stations are A and B. From station A you can travel to other stations in 14 ways(including one from A to B). From station B we can travel to A or other 13 stations ie you can travel from B to other stations in 14 ways. This is true for all the 15 stations.
Hence the number of ways in which a person can travel from every station to every other station is 15*14 = 210

Thus, number of tickets required = 210

Note: We come up with this solution since the question specifies "from EVERY station to EVERY other station". If the journey was only unidirectional:

There would be 14 ways to travel to other stations from the first station, 13 ways from the second station and so on.


Hope this helps :)