document.write( "Question 599207: An internet site requires a 6 character password made up of 2 digits followed by 4 letters where uppercase letters are not the same as lowercase letters. Without repetition of letters or numbers, how many different passwords can be created? \n" ); document.write( "

Algebra.Com's Answer #378878 by math-vortex(648) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hi, there--
\n" ); document.write( ".
\n" ); document.write( "number of ways to write first digit (0-9) = 10
\n" ); document.write( "number of ways to write second digit (0-9) = 10
\n" ); document.write( "number of ways to write the first letter (upper- or lowercase) = 52
\n" ); document.write( "number of ways to write the second letter (upper- or lowercase) = 52
\n" ); document.write( "number of ways to write the third letter (upper- or lowercase) = 52
\n" ); document.write( "number of ways to write the fourth letter (upper- or lowercase) = 52
\n" ); document.write( ".
\n" ); document.write( "In combinatorics, the fundamental principle of counting, states that if we have A ways of doing something and B ways of doing another thing, then there are A*B ways of performing both actions. So, we multiply the six numbers together:
\n" ); document.write( " $\"10%2A10%2A52%2A52%2A52%2A52=10%5E2%2B52%5E4=100%2A7311616=7311616\"$
\n" ); document.write( ".
\n" ); document.write( "There are 7,311,616 ways to create a password for the internet site.
\n" ); document.write( ".
\n" ); document.write( "Hoope this helps. Feel free to email me via gmail if you have questions about the solution.
\n" ); document.write( ".
\n" ); document.write( "Ms.Figgy
\n" ); document.write( "math.in.the.vortex@gmail.com \n" ); document.write( "

\n" );