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!.
