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  • A group of 6 books consists of 2 identical books on mathematics, 2 identical books on science, and 2 identical books on literature. In how many different ways can you arr

A group of 6 books consists of 2 identical books on mathematics, 2 identical books on science, and 2 identical books on literature. In how many different ways can you arrange the books on a shelf if the books of the same subject must be kept together?

 

Option: 1

5


Option: 2

8


Option: 3

3


Option: 4

4


Answers (1)

best_answer

To calculate the number of different ways the group of 6 books can be arranged on a 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 2 !, 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 2 !

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

2 ! \times 2 ! \times 2 !=2 \times 2 \times 2=8

Therefore, there are 8 different ways the group of 6 books can be arranged on the shelf, keeping the books of the same subject together.

Posted by

Divya Prakash Singh

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