Serial numbers for a product are to be made using 4 letters followed by 3 digits. The letters are to be taken from the first 8 letters of the alphabet, with no repeats. The digits are taken from the 10 digits $(0,1,2, \ldots, 9)$, with no repeats. How many serial numbers can be generated?

Step 1 ：The problem involves counting the number of ways to arrange a set of items, which is a common problem in combinatorics. The serial numbers are composed of two parts: the letters and the digits.

Step 2 ：For the letters, we have 8 options for the first letter, 7 options for the second letter (since we can't repeat), 6 options for the third letter, and 5 options for the fourth letter. So, the total number of ways to arrange the letters is \(8 \times 7 \times 6 \times 5 = 1680\).

Step 3 ：For the digits, we have 10 options for the first digit, 9 options for the second digit (since we can't repeat), and 8 options for the third digit. So, the total number of ways to arrange the digits is \(10 \times 9 \times 8 = 720\).

Step 4 ：The total number of serial numbers is the product of the number of options for the letters and the digits. So, the total number of serial numbers that can be generated is \(1680 \times 720 = 1209600\).

Step 5 ：Final Answer: The total number of serial numbers that can be generated is \(\boxed{1209600}\).