In a library, there are 5 distinct biology books, 7 distinct history books, and 3 distinct geography books that need to be organized on a shelf. How many unique arrangements can be made if the biology books are kept together?

Answer Choices

Correct answer marked below

5!*7!*3!

4!*5!*7!*3!

2*9!

5!*12!

5!*11!

Correct

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Explanation

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Official Explanation

Official

To keep all biology books together, we treat them as a single unit. Therefore, the total number of units to arrange is 7 (history) + 3 (geography) + 1 (the combined biology unit) = 11…

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Comments

2020MEB098Aug 30, 2024

Amazing

MohitaFeb 2, 2025

thanks!

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.