Question 1153320
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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.


<U>ANSWER</U>.  In all,  1680*5040 = 8467200 different serial numbers are possible.
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Solved.


Consider my solution as a MANTRA to solve other similar problems.


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From my solution, &nbsp;you should learn and understand


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    1)  how I used the fact that there are &nbsp;4 &nbsp;positions for letters and &nbsp;4 &nbsp;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.
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If you do understand it, then you understand the logic of the solution IN FULL.