Four books, one each in Chemistry, Physics, Biology and Mathematics are to be arranged in a shelf. In how many ways can this be done?

Options

A. 12
B. 36
C. 42
D. None of these

Answer

To solve the problem of arranging four books (Chemistry, Physics, Biology, and Mathematics) on a shelf, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Books**:
We have 4 books: Chemistry (C), Physics (P), Biology (B), and Mathematics (M).

2. **Determine the Number of Positions**:
Since we are arranging these books on a shelf, we need to find out how many different ways we can place these 4 books in 4 positions.

3. **Calculate the Arrangements**:
The number of ways to arrange 'n' distinct objects is given by the formula for permutations, which is n!.
Here, n = 4 (the number of books).
Therefore, the number of arrangements is:
\[ 4! = 4 \times 3 \times 2 \times 1 \]

4. **Perform the Calculation**:
Now, we calculate:
\[ 4! = 4 \times 3 = 12 \]
\[ 12 \times 2 = 24 \]
\[ 24 \times 1 = 24 \]

5. **Conclusion**:
Thus, the total number of ways to arrange the four books on the shelf is 24.

### Final Answer:
The number of ways to arrange the four books is **24**.

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