Question

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

• A. 92
• B. 90
• C. 91
• D. 93

Answer 1

The Correct Option is B

If there are 10 stations, the number of ways to choose two distinct stations (i.e., the number of possible journeys between two stations) is given by the combination formula \( \binom{n}{2} \), where \( n \) is the total number of stations.

Thus, the number of different journey tickets is:

\[ \binom{10}{2} = \frac{10 \times 9}{2} = 45 \]

This is the number of possible journeys in one direction. Since a ticket can be for a journey in either direction (forward or backward), we multiply by 2:

\[ 45 \times 2 = 90 \]

Thus, the number of different journey tickets required is 90.