Discussion
On a railway line there are 20 stops. A ticket is needed to travel between any 2 stops. How many different tickets would the government need to prepare to cater to all possibilities?
Answer: C
A ticket names a starting stop and a destination, so the two directions need different tickets: the order matters.
\[ {}^{20}P_{2} = 20 \times 19 = 380 \]
Treating the journey as unordered would give \( {}^{20}C_{2} = 190 \) - the number of station pairs, not of tickets.
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