There are $13$ stations between Chennai and Coimbatore. How many types of tickets must be printed so that a person can choose to travel between any of the two stations?
2026-03-27 10:12:06.1774606326
How many types of tickets must be printed so that a person can choose to travel between any of the two stations?
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This is similar to finding the diagonals of a tridecagon (13-sided polygon). The formula is $$\frac{n(n-3)}2$$
Plugging in $13$, we get $65$ different tickets.
EDIT: I forgot to consider going around the edge of the tridecagon itself, which gives us $13$ more tickets, or a total of $78$ tickets.
The above method was simply for visualization. Another way is simply to take ${13 \choose 2}$, or the ways in which you can choose two locations out of a total of thirteen locations. This will also give you $78$.