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 oneway journey?
1) 108
2) 14
3) 48
4) 96
On a railway route between two places A and B, there are 10
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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
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
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Current number of ticket options: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 oneway journey?
1) 108
2) 14
3) 48
4) 96
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].
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With 10 stations between A and B, the current route has 10 + 2 = 12 stations. Thus the current number of tickets for a oneway journey between two stations is 12P2 = 12 x 11 = 132. With the 4 new stations added, the number of tickets for a oneway journey between two stations will be 16P2 = 16 x 15 = 240 = (14 x 13)/2. Thus, the number of new tickets needed to be issued is 240  132 = 108.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 oneway journey?
1) 108
2) 14
3) 48
4) 96
Answer: A
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