Question

The number of ways that 5 Marathi, 3 English and 3 Tamil books be arranged if the books of each language are to be kept together is

• A. 25920
• B. 9250
• C. 5920
• D. 7480

Answer 1

The Correct Option is A

To solve the problem of arranging the books such that each language's books stay together, we begin by considering each language group as a single "block" or "unit". This results in three blocks: Marathi, English, and Tamil.

First, determine how many ways we can arrange these blocks among themselves. Since there are 3 blocks, they can be arranged in \(3!\) ways, which calculates as follows:

\(3! = 3 \times 2 \times 1 = 6\)

Next, arrange the books within each block. The number of ways to arrange the books within a block is given by the factorial of the number of books in that block:

1. For the 5 Marathi books, they can be arranged in \(5!\) ways: \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)

2. For the 3 English books, they can be arranged in \(3!\) ways: \(3! = 3 \times 2 \times 1 = 6\)

3. For the 3 Tamil books, they can also be arranged in \(3!\) ways: \(3! = 3 \times 2 \times 1 = 6\)

Thus, the total number of arrangements is the product of the ways to arrange the blocks and the ways to arrange the books within each block:

\(3! \times 5! \times 3! \times 3! = 6 \times 120 \times 6 \times 6\)

Calculating this gives:

\(6 \times 120 = 720\)

\(720 \times 6 = 4320\)

\(4320 \times 6 = 25920\)

Thus, the total number of ways to arrange the books, keeping each language's books together, is 25920.