In how many ways, 3 books can be given away to 7 boys, when each boy is eligible for any of the books?

Answer

To solve the problem of how many ways 3 books can be given away to 7 boys, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have 3 distinct books and 7 boys. Each boy can receive any of the books.

2. **Identifying the Distribution Method**: Since each book can go to any of the 7 boys independently, we can use the principle of multiplication to find the total number of ways to distribute the books.

3. **Calculating the Ways for Each Book**:
- For the first book, there are 7 choices (any of the 7 boys).
- For the second book, there are again 7 choices (any of the 7 boys).
- For the third book, there are also 7 choices (any of the 7 boys).

4. **Using the Multiplication Principle**: Since the choices for each book are independent, we multiply the number of choices together:
\[ \text{Total ways} = 7 \times 7 \times 7 = 7^3 \]

5. **Calculating \(7^3\)**:
- First, calculate \(7 \times 7 = 49\).
- Then, calculate \(49 \times 7 = 343\).

6. **Conclusion**: Therefore, the total number of ways to distribute the 3 books among the 7 boys is \(343\).

### Final Answer:
The total number of ways to give away 3 books to 7 boys is **343**.

---