10. In how many ways 5 Sanskrit 3 English and 3 Hindi books be arrange...
To find the number of ways to arrange the books, we need to consider the books of each language as a single entity. We can then arrange these entities along with the remaining individual books.
1. Arranging the books of the same language:
We have 5 Sanskrit books, 3 English books, and 3 Hindi books. We can arrange the Sanskrit books among themselves in 5! ways (5 factorial). Similarly, we can arrange the English books among themselves in 3! ways and the Hindi books in 3! ways.
2. Arranging the entities:
Now, we have 3 entities - Sanskrit books, English books, and Hindi books. We can arrange these entities among themselves in 3! ways.
3. Arranging the individual books:
Finally, we have 5 individual books remaining. We can arrange these books among themselves in 5! ways.
Therefore, the total number of ways to arrange the books is given by:
Total ways = (Arranging the books of the same language) x (Arranging the entities) x (Arranging the individual books)
Total ways = 5! x 3! x 3! x 5!
The correct option to represent this expression is (b) * 5!3!3!.
Explanation of Options:
(a) * 5!3!3!3! - This option includes an additional 3! for arranging the entities, which is incorrect.
(b) * 5!3!3! - This option correctly represents the expression mentioned above.
(c) 5P3 - This option represents the permutation of choosing 3 books from 5 books, which is not applicable in this scenario.
(d) None - This option is incorrect as there is a valid expression to represent the arrangement of the books.
In conclusion, the correct option is (b) * 5!3!3!, which represents the number of ways to arrange the books.
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