document.write( "Question 1011597: How many strings of 10 characters, such as \r
\n" ); document.write( "\n" ); document.write( "ABCPE1234F\r
\n" ); document.write( "\n" ); document.write( "can be made such that the first 5 characters are alphabet letters,
\n" ); document.write( "the next 4 are digits and the last character is a letter.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #627326 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "How many strings of 10 characters each, such as \r
\n" ); document.write( "\n" ); document.write( "ABCPE1234F\r
\n" ); document.write( "\n" ); document.write( "can be made such that the first 5 characters are alphabet letters,
\n" ); document.write( "the next 4 are digits and the last character is a letter.\r
\n" ); document.write( "\n" ); document.write( "(a) The characters may be repeated:
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Choose the 1st character 26 ways.\r\n" );
document.write( "Choose the 2nd character 26 ways.\r\n" );
document.write( "Choose the 3rd character 26 ways.\r\n" );
document.write( "Choose the 4th character 26 ways.\r\n" );
document.write( "Choose the 5th character 26 ways.\r\n" );
document.write( "Choose the 6th character 10 ways.\r\n" );
document.write( "Choose the 7th character 10 ways.\r\n" );
document.write( "Choose the 8th character 10 ways.\r\n" );
document.write( "Choose the 9th character 10 ways.\r\n" );
document.write( "Choose the 10th character 26 ways.\r\n" );
document.write( "\r\n" );
document.write( "That is 26×26×26×26×26×10×10×10×10×26 = 266104 = 3089157760000 ways:\r\n" );
document.write( "

\n" ); document.write( "(a) The characters may not be repeated:
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Choose the 1st character 26 ways.\r\n" );
document.write( "Choose the 2nd character 25 ways.\r\n" );
document.write( "Choose the 3rd character 24 ways.\r\n" );
document.write( "Choose the 4th character 23 ways.\r\n" );
document.write( "Choose the 5th character 22 ways.\r\n" );
document.write( "Choose the 6th character 10 ways.\r\n" );
document.write( "Choose the 7th character 9 ways.\r\n" );
document.write( "Choose the 8th character 8 ways.\r\n" );
document.write( "Choose the 9th character 7 ways.\r\n" );
document.write( "Choose the 10th character 21 ways.\r\n" );
document.write( "\r\n" );
document.write( "That is 26×25×24×23×22×10×9×8×7×21 = (26P6)×(10P4) = \r\n" );
document.write( "(165765600)×(5040) = 835458624000 ways.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );