Problem Solving

There are 10+2 = 12 stops along the line before the 4 new stops

Each of the 4 new stations then can go back and forth between these 12 stops, so 4x12x2 = 96 new one way tickets

Each of the 4 stations can go back and forth between each other. How many ways to select 2 stations from 4 = 4!/2! = 12

Total new one way tickets = 96 + 12 = 108, 1

mensanumber wrote:On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?

1) 108
2) 14
3) 48
4) 96

Current number of ticket options:
There are currently 12 stops: A, B, and the 10 stops between them.
Number of options for the departure stop = 12.
Number of options for the arrival stop = 11.
To combine these options, we multiply:
12*11 = 132.

New number of ticket options:
After 4 stops are added, the total number of stops will increase from 12 to 16.
Number of options for the departure stop = 16.
Number of options for the arrival stop = 15.
To combine these options, we multiply:
16*15 = 240.

New types of tickets:
(new number of ticket options) - (current number of ticket options) = 240 - 132 = 108.

The correct answer is [spoiler](1)[/spoiler].