Question

In how many ways can 7 English books, 8 Kannada books and 5 Hindi books be arranged in a shelf. In how many of these 

(a) All Kannada books are together. 

(b) No two English books are together. 

(c) Books of the same language are together, 

(d) All Kannada books are together and all Hindi books are

Answer 1

7 English + 8 Kannda + 5 Hindi = 20 books can be permutted in 20! Ways. 

(a) All Kannada books are together: Can be taken as 1 unit 

∴ 1K + 71 + 5H = 13 books can be permutted in 13! Ways and 8 Kannada books, they themselves can be arranged in 8! Ways 

∴ Total number of ways = 13!.8! 

(b) No two English books are together: Can be arranged between the other books 8K + 5H = 13 books can be arranged in 13! ways there are 14 places between 13 books we have to arrange 17 English books can be done in ¹⁴p, ways 

∴ The number of ways = 13!. ¹⁴P₇ 

(c) Books of the same language are together: 1 unit of E + 1 unit of K + 1 unit of H = 3 units of books can be done in 3! Ways. 7 English, 8 Kannada and 5 Hindi books they themselves can be done in 7!, 8! and 5! Ways 

∴ The total number of ways = 3! × 7! × 8! × 5!. 

(d) All Kannada books are together and Hindi books are together: 1 unit of Kannada + 1 unit of Hindi + 7 English = 9 can be done in 9! ways and 8 Kannada books and 5 Hindi books, they themselves can be arranged in 8! and 5! Respectively. 

∴ The total number of ways = 9! . 8! . 5!.