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  • A shelf contains 12 books, including 4 novels, 3 biographies, and 5 poetry books. If the books of each genre must be kept together, in how many different arrangements can

A shelf contains 12 books, including 4 novels, 3 biographies, and 5 poetry books. If the books of each genre must be kept together, in how many different arrangements can the books be placed on the shelf?

 

Option: 1

22,568

 


Option: 2

17,280

 


Option: 3

32,500

 


Option: 4

256,20


Answers (1)

best_answer

To calculate the number of different arrangements of the books on the shelf, considering that books of the same genre must be kept together, we can treat each genre of books as a single entity.

There are 3 different genres: novels, biographies, and poetry books. We need to arrange these 3 entities on the shelf.

The number of ways to arrange the novels among themselves is given by 4 !, the number of ways to arrange the biographies among themselves is given by 3 !, and the number of ways to arrange the poetry books among themselves is given by 5 !.

Therefore, the total number of different arrangements of the books on the shelf, with the books of each genre kept together, is:

\mathrm{4 ! \times 3 ! \times 5 !=24 \times 6 \times 120=17,280.}

Therefore, there are 17,280 different arrangements in which the books can be placed on the shelf, keeping the books of each genre together.

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