What is the number of ways in which one can post 5 letters in 7 letters boxes ?

Options

A. `7^(5)`
B. `3^(5)`
C. `5^(7)`
D. 2520

Answer

To solve the problem of how many ways one can post 5 letters in 7 letter boxes, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have 5 letters and 7 boxes. Each letter can be placed in any of the 7 boxes.

2. **Choices for Each Letter**: For each letter, there are 7 possible boxes to choose from.

3. **Calculate Total Combinations**: Since the choice of box for each letter is independent of the others, we can use the multiplication principle of counting. This means we multiply the number of choices for each letter together.
- For the first letter, there are 7 choices.
- For the second letter, there are also 7 choices.
- This continues for all 5 letters.

4. **Mathematical Representation**: The total number of ways to post the letters can be represented mathematically as:
\[ \text{Total Ways} = 7 \times 7 \times 7 \times 7 \times 7 = 7^5 \]

5. **Calculate \(7^5\)**: Now we need to compute \(7^5\):
\[ 7^5 = 16807 \]

6. **Final Answer**: Therefore, the total number of ways to post 5 letters in 7 letter boxes is **16807**.