Question

5 books in Math and 3 books in Physics are placed on a shelf so that the books on the same subject always remain together. The possible arrangements are

• A. 1440
• B. 1956
• C. 720
• D. None of these

Hint:

When objects must be grouped together, treat the groups as single units first, then arrange within the group.

Answer 1

The Correct Option is A

Step 1: Understand the arrangement condition.
Since the books on each subject must remain together, we can treat the entire set of Math books and the set of Physics books as individual "blocks".
Thus, we have 2 "blocks" (one for Math and one for Physics).
Step 2: Calculate the number of ways to arrange the blocks.
These 2 blocks can be arranged in \( 2! \) ways.
This is because we can place the Math block first or the Physics block first.
Step 3: Calculate the number of arrangements within each block.
The 5 Math books can be arranged in \( 5! \) ways within their block.
The 3 Physics books can be arranged in \( 3! \) ways within their block.

Step 4: Total number of arrangements.
The total number of arrangements is: \[ 2! \times 5! \times 3! = 2 \times 120 \times 6 = 1440 \]
Step 5: Conclusion. Therefore, the total number of arrangements is 1440, which is option (a).