Multiple choice

In a library, 12 books are to be arranged such that a particular pair of books should always be together. In how many ways can the books be arranged?

  1. 12! × 2!

  2. 9! × 3!

  3. 10! × 2!

  4. 11! × 2!

  5. 11! + 2!
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D Correct answer
Explanation

Treat the pair of books as one unit. Now we have 11 units to arrange, which is 11!. Within the pair, the 2 books can be arranged in 2! ways. Total ways = 11! * 2!.

AI explanation

Treat the particular pair of books that must be together as a single entity. Along with the other 10 books, this creates a total of 11 entities to arrange, which can be done in 11! ways. The pair of books can also be arranged internally in 2! ways, so the total arrangements are 11! multiplied by 2!.

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