Question

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

• A. 92
• B. 90
• C. 91
• D. None of these

Answer 1

The Correct Option is B

To determine the number of different journey tickets required for 10 stations, we consider that for each pair of stations, one ticket is needed. If there are 10 stations, we need to calculate the number of unique station pairs. The formula for the number of combinations of choosing 2 stations out of 10 is given by the binomial coefficient:
$$\binom{n}{r} = \frac{n!}{r!(n-r)!}$$
where \( n \) is the total number of stations, and \( r \) is the number of stations to choose.

Using the formula:
$$\binom{10}{2} = \frac{10!}{2!(10-2)!} = \frac{10 \times 9}{2 \times 1} = 45$$
This result (45) represents the number of unique pairs of stations, i.e., journeys from one station to another.

Since each journey involves traveling from one station to another and returning, we need to account for both outbound and return tickets. Therefore, we multiply this number by 2:
$$45 \times 2 = 90$$

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