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I am writing a computer program which generate 5 digit alpha-numeric codes. Each character can contain a-z,A-Z and 0-9 (62 different possibility per character).

So if there are 5 character how many possibility are there?

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You can get $62^5$ (or $916132832$) possibilities.

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Every character can have $62$ different possibility as you said, so the total possible combinations of 5 character would be $62\times62\times62\times62\times62=62^5$.

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