5 letters can be posted into 3 letter boxes in:

Options

A. `3^(5)` ways
B. `5^(3)` ways
C. `""^(5)C_(3)` ways
D. none

Answer

To solve the problem of how many ways 5 letters can be posted into 3 letter boxes, we can break it down step by step:

### Step-by-Step Solution:

1. **Identify the Variables**:
- We have 5 letters (let's denote them as L1, L2, L3, L4, L5).
- We have 3 letter boxes (let's denote them as B1, B2, B3).

2. **Determine the Choices for Each Letter**:
- Each letter can be placed in any of the 3 letter boxes. This means for each letter, there are 3 choices.

3. **Calculate the Total Choices**:
- Since the choices for each letter are independent of the others, we multiply the number of choices for each letter.
- For L1, there are 3 choices (B1, B2, or B3).
- For L2, there are also 3 choices.
- This pattern continues for L3, L4, and L5.
- Therefore, the total number of ways to post the letters is:
\[ \text{Total Ways} = 3 \times 3 \times 3 \times 3 \times 3 = 3^5 \]

4. **Calculate \(3^5\)**:
- Now we calculate \(3^5\):
\[ 3^5 = 243 \]

5. **Conclusion**:
- Thus, the total number of ways to post the 5 letters into the 3 letter boxes is **243**.

### Final Answer:
The total number of ways to post 5 letters into 3 letter boxes is **243**.