.
Any one of the first 8 letters in the 1-st position gives 8 options.
Any one of the REMAINING 7 of the first 8 letters in the 2-nd position gives 7 options.
Any one of the REMAINING 6 of the first 8 letters in the 3-rd position gives 6 options.
Any one of the REMAINING 5 of the first 8 letters in the 4-th position gives 8 options.
Thus with 4 letters in the first 4 positions, you have 8*7*6*5 = 1680 options.
Same analysis works for digits in the following 4 positions, giving 10*9*8*7 = 5040 options.
These options are independent, giving 1680*5040 all possible serial numbers.
ANSWER. In all, 1680*5040 = 8467200 different serial numbers are possible.
Solved.
Consider my solution as a MANTRA to solve other similar problems.
---------------
From my solution, you should learn and understand
1) how I used the fact that there are 4 positions for letters and 4 positions for digits ?
- Each of these facts gave me 4 factors to a product.
2) how I used the fact that there was no repeating for letters and digits ?
- Each of these facts provided DECREASING factors in the products.
3) how I used the fact that the letters were taken from the first 8 letters
and how I used the fact that the digits were from 0 to 9?
- It provided me the first factor of 8 for the letters and the first factor of 10 for the digits.
If you do understand it, then you understand the logic of the solution IN FULL.