In how many ways can 4 letters be posted in 5 letter boxes?

Answer

To solve the problem of how many ways 4 letters can be posted in 5 letter boxes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have 4 letters and 5 letter boxes. Each letter can be placed in any of the 5 boxes.

2. **Choices for Each Letter**: For each letter, there are 5 possible choices (the 5 letter boxes).

3. **Calculating Total Combinations**: Since the placement of each letter is independent of the others, we can multiply the number of choices for each letter.
- For the 1st letter, there are 5 choices.
- For the 2nd letter, there are also 5 choices.
- For the 3rd letter, there are again 5 choices.
- For the 4th letter, there are still 5 choices.

4. **Using Exponents**: Therefore, the total number of ways to post the letters can be expressed as:
\[ \text{Total Ways} = 5 \times 5 \times 5 \times 5 = 5^4 \]

5. **Calculating \(5^4\)**: Now, we calculate \(5^4\):
\[ 5^4 = 625 \]

6. **Final Answer**: Thus, the total number of ways to post 4 letters in 5 letter boxes is **625**.