Permutation

Probability Level 2

If there are 25 railway stations on a railway line, how many types of single second-class tickets must be printed, so as to enable a passenger to travel from one station to another?

The answer is 600.

4 solutions

Nick Byrne
Jan 19, 2016

There are 25 stations, call them A, B, C, ... , X, Y

From a station to any of the others, there are 24 possible tickets.

1: n/a, AB, AC, ... , AX, AY.

2: BA, n/a, BC, ... , BX, BY.

...

24: XA, XB, XC, ... , n/a, XY.

25: YA, YB, YC, ... , YX, n/a.

Note: AB $\neq$ BA

Hence the total number of unique tickets is $25 \times 24 = \boxed{600}$

Replying to @Kislay Kashyap: The tickets in the other direction are included 25!/(25-2)! = 600 which incudes all "flipped" pairs.

Mariusz Popieluch - 1 year, 3 months ago

I did not consider the second case of reverse trains

Bipul Kumar - 1 week, 4 days ago

we also have to include the tickets for return journey . so 600 * 2 = 1200

Kislay Kashyap - 4 years, 3 months ago

It is already specified by Byrne, no. Of unique tickets and AB not equal to BA.. So 600 is only the answer!

Prem Chebrolu - 2 years, 10 months ago

Seungjin Baek
Mar 16, 2017

It's like picking two stations from 25 stations. The order of (start & destination) stations matter, i.e. A->B is not same as B-> A. Therefore, we use permutation of picking two out of 25. 2P25 = 25!/23! = 25*24 = 600

That's how I approached it :) Also, good explanation!

Mariusz Popieluch - 1 year, 3 months ago

Prateek Mishra
Jul 28, 2017

On a ticket there can be 2 stations source and destination, there are 25 choices for the 1st and 24 choices for the second. Total types of tickets printed is 25*24 = 600

Ramiel To-ong
Jan 19, 2016

nice solution Byrne

Permutation

The answer is 600.

4 solutions

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