There are 10 stations along a railway line. How many different one-way journey tickets (from one station to a different station) are needed by the authorities?

Introduction / Context:Each one-way ticket is specified by an ordered pair (start, destination) with start ≠ destination. We count ordered choices.

Given Data / Assumptions:

• 10 stations labeled distinctly.
• Tickets are one-way (direction matters).

Concept / Approach:For each start station, any of the remaining 9 stations can be the destination. Sum (or multiply) across starts.

Step-by-Step Solution:Choices = 10 × 9 = 90.

Verification / Alternative check:Unordered pairs would be C(10, 2) = 45; direction doubles this to 90, consistent with 10 × 9.

Why Other Options Are Wrong:91 and 92/93 are off by +1/+2/+3; 100 counts invalid same-station tickets.

Common Pitfalls:Confusing one-way with round-trip or unordered counting.

Final Answer:90