Books of two subjects — Aptitude Question
Books of two subjects: In how many ways can 4 maths books and 3 physics books be arranged on a shelf so that all… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
In how many ways can 4 maths books and 3 physics books be arranged on a shelf so that all the maths books stay together?
Options
- 144
- 288
- 576
- 720
Show the answer and the worked solution
Correct answer: C. 576
Worked solution
- The maths block plus 3 physics books = 4 items, arranged in 4! = 24 ways.
- Within the block, 4 maths books arrange in 4! = 24 ways.
- Total = 24 × 24 = 576.
Answer: 576.
The idea
Group, arrange the groups, then arrange within the group. The two factorials multiply.
Shortcut. A block of 4 on a 7-slot shelf can start in 4 places; then 4! orders inside the block and 3! for the physics books: 4 × 24 × 6 = 576.
Common trap. "144" — arranging the maths books (4!) and the physics books (3!) but forgetting that the maths block itself can sit in 4 different places.
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