document.write( "Question 1204448: You own 12 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #840702 by ikleyn(52816) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "You own 12 CDs. You want to randomly arrange 5 of them in a CD rack.
\n" ); document.write( "What is the probability that the rack ends up in alphabetical order?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The number of all different ordered quintuples of five CDs from twelve CDs is  \r\n" );
document.write( "\r\n" );
document.write( "    total = 12*11*10*9*8.    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of all different quintuples of 5 CDs from 12 CDs is \r\n" );
document.write( "\r\n" );
document.write( "     =  =   \r\n" );
document.write( "\r\n" );
document.write( "(without looking in ordering - same as the number of combinations  ).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of all different ORDERED quintuples of 5 CDs from 12 CDs is \r\n" );
document.write( "\r\n" );
document.write( "     =     (2)\r\n" );
document.write( "\r\n" );
document.write( "(without looking in ordering).  Notice that number (2) is the same as number (1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When we estimate the number of alphabetically ordered quintuples among all ordered quintuples (2),\r\n" );
document.write( "we should divide the number (2) by 5!, because among 5! permutations only one is ordered alphabetically.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, from the number of all ordered quintuples (1) or (2), the number of those ordered alphabetically is\r\n" );
document.write( "\r\n" );
document.write( "    favorable =  = .    (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The problem asks about the probability  \r\n" );
document.write( "\r\n" );
document.write( "    P =  =  =  =  =  = .    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );