Permutations
The number of ways in which 5 boys and 3 girls can be arranged in a row so that all girls sit together is
Select the correct option:
Solution
4320
- Grouping Strategy: Treat the 3 girls as a single 'block' or unit.
- Arrange the Units:
- We now have 5 boys + 1 block of girls = 6 units.
- Arrangement of 6 distinct units = 6!=720.
- Internals of Block: The 3 girls within the block can be arranged among themselves in 3! ways.
- 3!=6.
- Total Calculation:
- Total Ways =6!×3!
- =720×6=4,320.
- Result: 4,320 ways.
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- permutations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
4320
- Grouping Strategy: Treat the 3 girls as a single 'block' or unit.
- Arrange the Units:
- We now have 5 boys + 1 block of girls = 6 units.
- Arrangement of 6 distinct units = 6!=720.
- Internals of Block: The 3 girls within the block can be arranged among themselves in 3! ways.
- 3!=6.
- Total Calculation:
- Total Ways =6!×3!
- =720×6=4,320.
- Result: 4,320 ways.
This medium difficulty mathematics question is from the chapter permutations and combinations, covering the topic of permutations. It appeared in the 2025 exam.
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