The number of ways in which 7 different books can be given to 5 students if each can receive none, one or more books is

Options

A. A) `5^7`
B. B) `7^5`
C. C) `""^(11)C_5`
D. D) `12!`

Answer

To solve the problem of distributing 7 different books to 5 students where each student can receive none, one, or more books, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Choices for Each Book**:
Each of the 7 different books can be given to any of the 5 students.

2. **Determine the Number of Choices per Book**:
For each book, there are 5 choices (one for each student).

3. **Calculate the Total Choices for All Books**:
Since the choice for each book is independent of the others, we can multiply the number of choices for each book. Therefore, for 7 books, the total number of ways to distribute them is:
\[ 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5^7 \]

4. **Compute the Value of \(5^7\)**:
Now, we can calculate \(5^7\):
\[ 5^7 = 78125 \]

5. **Conclusion**:
Thus, the total number of ways in which 7 different books can be given to 5 students is \(78125\).

### Final Answer:
The number of ways in which 7 different books can be given to 5 students is **78125**.

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