SOLUTION: Standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers. How many different standard plates are possible in this problem?

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Question 1182393: Standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers.
How many different standard plates are possible in this problem?
(Assume that repartitions of letters and numbers are allowed.)
Answer by ikleyn(52852) About Me  (Show Source):
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Standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers.
How many different standard plates are possible in this problem?
(Assume that highlight%28cross%28repartitions%29%29 repetitions of letters and numbers are allowed.)
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   10 options in the 1st position;

   10 options in the 2nd position;

   26 options in the 3rd position

      . . . and so on . . . 


In all,  10^2 * 26^3 * 10^2 = 175760000  different plates are possible.    ANSWER

Solved, answered and explained.