<p>In a network of railways, a small island has 15 stations. Find the number of different types of tickets to be printed for each class, if every station must have tickets for other stations.</p>
Step-by-Step Solution
Key Concept: Each ticket is unidirectional (from station A to station B is different from B to A), so we need ordered pairs of distinct stations. This is a permutation problem: P(n,2) = n(n-1).
<p><strong>Step 1:</strong> Identify what we're counting. Each ticket specifies a journey FROM one station TO another station. This is an ordered pair (origin, destination) where origin ≠ destination.</p><p><strong>Step 2:</strong> Since direction matters, a ticket from Station A to Station B is different from a ticket from Station B to Station A.</p><p><strong>Step 3:</strong> For the origin station, we have 15 choices.</p><p><strong>Step 4:</strong> For the destination station, we have 14 choices (any station except the origin).</p><p><strong>Step 5:</strong> Total number of different tickets = 15 × 14 = 210</p><p><strong>Alternatively:</strong> This is P(15,2) = 15!/(15-2)! = 15 × 14 = 210</p><p>∴ Answer: <strong>210</strong></p>
Correct Answer: 210