Question:
There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is
There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is
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A ticket from A to B differs from a ticket from B to A, so count ordered pairs of stations, not unordered pairs.
Updated On: Jul 14, 2026
- 10!
- 90
- 81
- 10
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The Correct Option is B
Solution and Explanation
Step 1: A ticket from A to B differs from B to A.
Each ticket has a starting and ending station.
Step 2: This is a permutation problem.
Choosing 2 stations out of 10 where order matters.
Step 3: Apply the formula.
10P2 = 10 x 9 = 90
Step 4: Why other options are wrong.
10! is far too large; 81 has no meaning here; 10 only counts one ticket per station.
Final Answer: The authorities need 90 different journey tickets.
Each ticket has a starting and ending station.
Step 2: This is a permutation problem.
Choosing 2 stations out of 10 where order matters.
Step 3: Apply the formula.
10P2 = 10 x 9 = 90
Step 4: Why other options are wrong.
10! is far too large; 81 has no meaning here; 10 only counts one ticket per station.
Final Answer: The authorities need 90 different journey tickets.
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