A car company is going to issue new ID codes to its employees. Each code will have one digit followed by four letters. The letter v and the digits 3, 4, and 5 will not be used. So, there are 25 letters and 7 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?

To calculate the total number of possible employee ID codes, we can use the Fundamental Counting Principle which states that if there are [tex]m[/tex] ways to do one thing and [tex]n[/tex] ways to do another thing, then there are [tex]m\times n[/tex] ways to do both things together.

Given that each employee ID code will have one digit followed by four letters, we simply need to calculate how many options there are for each part of the combination, then multiply them to find the total number of combinations.

For the first digit, there are 7 options (0, 1, 2, 6, 7, 8, 9) because 3, 4, and 5 are not used.

For each of the four letters following the first digit, there are 25 options because there are 25 letters available, and repetition is allowed.

Therefore, the total number of possible ID codes can be calculated as:

7 × 25 × 25 × 25 × 25 = 2,734,375

So 2,734,375 employee ID codes can be generated.