SOLUTION: In the olden days, computer file names were limited to 13 characters. They were case sensitive ("A" and "a" are considered distinct) and there were some other rules. Assuming tha

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Question 1154280: In the olden days, computer file names were limited to 13 characters. They were
case sensitive ("A" and "a" are considered distinct) and there were some other
rules. Assuming that file names are limited to 13 characters, which are either
digits or letters, that the letters are case sensitive, and that no file name
can start with a number, how many possible file names are there?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The usable characters are these: 26 capital letters, 26 lower case letters and
10 digits.  That's the 62 characters below.

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789

We choose the first character as any of the 52 letters.
The other characters can be any of the 62.

There are 52 ways to choose a 1-character file name.
There are 52∙62 ways to choose a 2-character file name.
There are 52∙622 ways to choose a 3-character file name.
There are 52∙623 ways to choose a 4-character file name.
There are 52∙624 ways to choose a 5-character file name.
There are 52∙625 ways to choose a 6-character file name.
There are 52∙626 ways to choose a 7-character file name.
There are 52∙627 ways to choose a 8-character file name.
There are 52∙628 ways to choose a 9-character file name.
There are 52∙629 ways to choose a 10-character file name.
There are 52∙6210 ways to choose a 11-character file name.
There are 52∙6211 ways to choose a 12-character file name.
There are 52∙6212 ways to choose a 13-character file name.

That's 52+52∙622+52∙623+52∙624+52∙625+52∙626+52∙627+52∙628+52∙629+52∙6210+52∙6211+52∙6212 ways

52(1+622+623+624+625+626+627+628+629+6210+6211+6212+6213 ways


That's 52 times a geometric series with a1 = 1, n=13, r=62.



 



170516131835587361034172

That's the answer. [A 22-digit number!!!]

Edwin
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