.
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 OR 3 identical digits.
With 26 capital letters of English alphabet and 10 digits there are
= 17576000
combinations of 3 letters and 10 digits.
Of them, there are = 26000 prohibited combinations containing 3 identical letters and
= 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
- - + 260 = 17576000 - 26000 - 175760 + 260 = 17374500
represents the number of all allowed plates.
Answer. The total number of possible license plates is 17374500.