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how many license plates of 3 symbols (letters and digits) can be made using at least 2 letters for each?

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To create a license plate with at least 2 letters, there are two cases to consider: 2 letters and 1 digit, or 3 letters.

Case 1: 2 letters and 1 digit
There are 26 choices for each letter (A-Z) and 10 choices for each digit (0-9).
The license plate can be in the form LLD, LDL, or DLL (L = letter, D = digit).
So, the number of license plates for this case is:
(26 * 26 * 10) + (26 * 10 * 26) + (10 * 26 * 26) = 3 * 26^2 * 10 = 20,280

Case 2: 3 letters
There are 26 choices for each letter (A-Z).
The number of license plates for this case is:
26 * 26 * 26 = 26^3 = 17,576

To find the total number of license plates, add the possibilities from both cases:
20,280 + 17,576 = 37,856

So, there are 37,856 possible license plates with at least 2 letters.
User Mohamed Sabry
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