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  • A bookshelf has space for 8 books, with 3 books on mathematics, 2 books on science, and 3 books on literature. In how many different ways can you arrange the books on the

A bookshelf has space for 8 books, with 3 books on mathematics, 2 books on science, and 3 books on literature. In how many different ways can you arrange the books on the shelf if the books of the same subject must be kept together?

 

Option: 1

63


Option: 2

74


Option: 3

54


Option: 4

72


Answers (1)

To calculate the number of different ways the books can be arranged on the shelf, with the books of the same subject kept together, we can treat each subject group as a single entity.

Since there are 3 subject groups (mathematics, science, and literature), we need to arrange these 3 entities on the shelf.

The number of ways to arrange the mathematics books among themselves is given by 3 !, the number of ways to arrange the science books among themselves is given by 2 !, and the number of ways to arrange the literature books among themselves is given by 3 !.

Therefore, the total number of different ways to arrange the books on the shelf, with the books of the same subject kept together, is:

3 ! \times 2 ! \times 3 !=6 \times 2 \times 6=72 .

Therefore, there are 72 different ways the books can be arranged on the shelf, keeping the books of the same subject together.

Posted by

Ramraj Saini

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