Multiple choice

In how many ways can 5 Physics, 3 Chemistry and 3 Maths books be arranged, keeping the books of the same subject together?

  1. 5! x 3! x 3!

  2. 5P3

  3. 5! x 3!

  4. 5! x 3! x 3! x 3!
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Arrange the 3 subjects as blocks: 3! ways. Within each block, books can be arranged: 5! for Physics, 3! for Chemistry, 3! for Maths. Total = 3! * 5! * 3! * 3!.

AI explanation

We treat the books of each subject as a single connected block, which means there are 3 blocks to arrange in 3! ways. The 5 Physics books can be arranged within their block in 5! ways, while the 3 Chemistry books can be arranged in 3! ways, and the 3 Maths books can also be arranged in 3! ways. Multiplying all these together gives 3! multiplied by 5! multiplied by 3! multiplied by 3!, which simplifies to 5! x 3! x 3! x 3!.

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