There are 20 stops for the local trains running between Churchgate and Virar. A passenger travelling between any two stops needs to buy a ticket. How many types of tickets are required to be made to meet all the possibilities?

We need to SELECT people.
[SELECT = Combination = ⁿC_r = n!/r!(n-r)!

There are 20 stations. A ticket is needed between 2 stops.
That means, we simply need to select 2 stops from possible 20 stops.

That can be done by ²⁰C₂ = 20!/2!(20 - 2)! = 20!/2!18! = 190 ways.

This is when we start from one side.
When we travel from the other side we will need a separate ticket.
That means while going from A to B and B to A, we will need separate tickets.
So again on another side, we need 190 tickets.

Total tickets = 190 + 190 = 380 tickets.