P & C - 3 (SNAP-2008)

There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is 

                          

(A)  10!       (B)  90       (C) 81        (D) 45   (E) 10

Solution follows here:

Solution:

Let the stations be A B C D E F G H I J K

First note that - a journey ticket is always considered between two points. So we need to make two selections out of the given 10.

The journey tickets may be for (A to B) or (B to A) or (A to C) or (C to A) etc..,

We are considering reverse order also in order to facilitate reverse journey possibilities. So note that here order is also coming into picture along with the

selection of stations. Hence we need to go for permutations instead of combinations.

The number of different journey tickets = 10P2 = 10 * 9 = 90

Answer is (B)