Question 1117919
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The solution is to consider ALL possible combinations of 3 letters  and 10 digits and then to subtract those combinations that 

contain  3 identical letters  <U>OR</U>  3 identical digits.


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With 26 capital letters of English alphabet and 10 digits there are 

    {{{26^3*10^3}}} = 17576000 

combinations of 3 letters  and 10 digits.



Of them, there are  {{{26*10^3}}} = 26000 prohibited combinations containing 3 identical letters and

                    {{{26^3*10}}} = 175760 prohibited combinations containing 3 identical digits.



These two sets of 26000 elements  and  175760 elements have the intersection consisting of 26*10 = 260 elements that we counted twice.



Therefore, the alternate difference 

    {{{26^3*10^3}}} - {{{26*10^3}}} - {{{26^3*10}}} + 260 = 17576000 - 26000 - 175760 + 260 = 17374500

represents the number of all allowed plates.



<U>Answer</U>.  The total number of possible license plates is  17374500.
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