Question:easy
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
Show Hint
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
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: Count unordered pairs first.
10C2 = 45 distinct pairs of stations, meaning 45 distinct routes.
Step 2: Account for direction.
Each route needs 2 tickets, one per direction.
Step 3: Multiply.
45 x 2 = 90
Final Answer: 90 different tickets are needed.
10C2 = 45 distinct pairs of stations, meaning 45 distinct routes.
Step 2: Account for direction.
Each route needs 2 tickets, one per direction.
Step 3: Multiply.
45 x 2 = 90
Final Answer: 90 different tickets are needed.
Was this answer helpful?
0
Top Questions on permutations and combinations
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- Mathematics
- permutations and combinations
- How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
- BITSAT - 2025
- Mathematics
- permutations and combinations
- A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain gluten, while the rest are gluten-free.
One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went to the same restaurant: they planned to choose two different vegetarian items and one non-vegetarian item only from the gluten-free options. The number of item combinations that Rohit and his friends could choose from, given their plan, was 12 times the number of item combinations that Bela and her friends could choose from, given their plan.
How many menu items contain gluten?- XAT - 2024
- Quantitative Ability and Data Interpretation
- permutations and combinations
- Five people are distributed in four identical rooms. A room can also contain zero people. Find the number of ways to distribute them.
- JEE Main - 2024
- Mathematics
- permutations and combinations
- Want to practice more? Try solving extra ecology questions todayView All Questions
Questions Asked in SNAP exam
In the following figure, the smaller triangle represents teachers; the big triangle represents politicians; circle represents graduates and rectangle represents members of Parliament. Different regions are being represented by letters of English alphabet. On the basis of the above diagram, answer the following questions: 
- SNAP - 2024
- Venn Diagrams