A code consists of two letters of the alphabet followed by 5 digits .How many such codes are possible ?

Options

A. 7
B. 10
C. 128
D. `67,600,000`

Explanation

To solve the problem of how many codes can be formed with two letters followed by five digits, we can break it down into steps.

### Step-by-Step Solution:

1. **Identify the components of the code**:
The code consists of two letters followed by five digits.

2. **Determine the number of choices for the letters**:
- There are 26 letters in the English alphabet.
- For the first letter, we have 26 choices.
- For the second letter, we again have 26 choices.
- Therefore, the total number of combinations for the letters is:
\[ 26 \times 26 = 676 \]

3. **Determine the number of choices for the digits**:
- There are 10 possible digits (0 through 9).
- For each of the five digit positions, we have 10 choices.
- Therefore, the total number of combinations for the digits is:
\[ 10 \times 10 \times 10 \times 10 \times 10 = 10^5 = 100000 \]

4. **Combine the choices for letters and digits**:
- Since the letters and digits are independent of each other, we multiply the number of combinations for the letters by the number of combinations for the digits:
\[ 676 \times 100000 = 67600000 \]

5. **Final answer**:
The total number of possible codes is:
\[ 676 \times 10^5 = 67600000 \]

### Final Result:
The total number of codes possible is **67,600,000**.