SOLUTION: A license plate consists of 3 letters followed by 3 digits. What is the total number of possible license plates if a letter or digit can be used twice?

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Question 1117919: A license plate consists of 3 letters followed by 3 digits. What is the total number of possible license
plates if a letter or digit can be used twice?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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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 OR 3 identical digits. 

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

    26%5E3%2A10%5E3 = 17576000 

combinations of 3 letters  and 10 digits.



Of them, there are  26%2A10%5E3 = 26000 prohibited combinations containing 3 identical letters and

                    26%5E3%2A10 = 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%5E3%2A10%5E3 - 26%2A10%5E3 - 26%5E3%2A10 + 260 = 17576000 - 26000 - 175760 + 260 = 17374500

represents the number of all allowed plates.



Answer.  The total number of possible license plates is  17374500.