Question:
A teacher has 2 different books on English, 3 different books on physics, and 4 different books on mathematics. These books are to be placed on the shelf so that all books of the same subjects are together. The number of different ways this can be done is:
A teacher has 2 different books on English, 3 different books on physics, and 4 different books on mathematics. These books are to be placed on the shelf so that all books of the same subjects are together. The number of different ways this can be done is:
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Treat each subject as one block, arrange the blocks, then arrange books inside each block.
Updated On: Nov 12, 2026
- \(1278\)
- \(1728\)
- \(1872\)
- \(1782\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The books of each subject form a block, giving three blocks.
Step 2: Arrange the Blocks
Three blocks can be arranged in \(3!=6\) ways.
Step 3: Arrange Within Blocks
English: \(2!=2\), Physics: \(3!=6\), Mathematics: \(4!=24\).
Step 4: Multiply
Total \(=6\times2\times6\times24=1728\), option (B).
Final Answer:
The number of ways is 1728. \[ \boxed{\text{(B) }1728} \]
The books of each subject form a block, giving three blocks.
Step 2: Arrange the Blocks
Three blocks can be arranged in \(3!=6\) ways.
Step 3: Arrange Within Blocks
English: \(2!=2\), Physics: \(3!=6\), Mathematics: \(4!=24\).
Step 4: Multiply
Total \(=6\times2\times6\times24=1728\), option (B).
Final Answer:
The number of ways is 1728. \[ \boxed{\text{(B) }1728} \]
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