document.write( "Question 1154280: In the olden days, computer file names were limited to 13 characters. They were
\n" ); document.write( "case sensitive (\"A\" and \"a\" are considered distinct) and there were some other
\n" ); document.write( "rules. Assuming that file names are limited to 13 characters, which are either
\n" ); document.write( "digits or letters, that the letters are case sensitive, and that no file name
\n" ); document.write( "can start with a number, how many possible file names are there? \n" ); document.write( "
Algebra.Com's Answer #776682 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
The usable characters are these: 26 capital letters, 26 lower case letters and\r\n" );
document.write( "10 digits.  That's the 62 characters below.\r\n" );
document.write( "\r\n" );
document.write( "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789\r\n" );
document.write( "\r\n" );
document.write( "We choose the first character as any of the 52 letters.\r\n" );
document.write( "The other characters can be any of the 62.\r\n" );
document.write( "\r\n" );
document.write( "There are 52 ways to choose a 1-character file name.\r\n" );
document.write( "There are 52∙62 ways to choose a 2-character file name.\r\n" );
document.write( "There are 52∙622 ways to choose a 3-character file name.\r\n" );
document.write( "There are 52∙623 ways to choose a 4-character file name.\r\n" );
document.write( "There are 52∙624 ways to choose a 5-character file name.\r\n" );
document.write( "There are 52∙625 ways to choose a 6-character file name.\r\n" );
document.write( "There are 52∙626 ways to choose a 7-character file name.\r\n" );
document.write( "There are 52∙627 ways to choose a 8-character file name.\r\n" );
document.write( "There are 52∙628 ways to choose a 9-character file name.\r\n" );
document.write( "There are 52∙629 ways to choose a 10-character file name.\r\n" );
document.write( "There are 52∙6210 ways to choose a 11-character file name.\r\n" );
document.write( "There are 52∙6211 ways to choose a 12-character file name.\r\n" );
document.write( "There are 52∙6212 ways to choose a 13-character file name.\r\n" );
document.write( "\r\n" );
document.write( "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\r\n" );
document.write( "\r\n" );
document.write( "52(1+622+623+624+625+626+627+628+629+6210+6211+6212+6213 ways\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's 52 times a geometric series with a1 = 1, n=13, r=62.\r\n" );
document.write( "\r\n" );
document.write( "\"S%5Bn%5D=a%5B1%5D%28r%5En-1%29%2F%28r-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"S%5B13%5D=1%2862%5E13-1%29%2F%2862-1%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"52%2A3279156381453603096811\"\r\n" );
document.write( "\r\n" );
document.write( "170516131835587361034172\r\n" );
document.write( "\r\n" );
document.write( "That's the answer. [A 22-digit number!!!]\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );