document.write( "Question 957399: If all the distinguishable arrangements of the word \"tutor\" were listed in
\n" ); document.write( "alphabetical order and numbered #1,#2,#3,..., what would be the number of the
\n" ); document.write( "arrangement \"tutor\"? \n" ); document.write( "

Algebra.Com's Answer #585530 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
If all the distinguishable arrangements of the word \"tutor\" were listed in
\n" ); document.write( "alphabetical order and numbered #1,#2,#3,..., what would be the number of the
\n" ); document.write( "arrangement \"tutor\"?
\n" ); document.write( "

\r\n" );
document.write( "There are  distinguishable arrangements of \"tutor\".\r\n" );
document.write( "\r\n" );
document.write( "The letters in \"tutor\" in alphabetical order are \"o\",\"r\",\"t\",\"t\",u\". So\r\n" );
document.write( "arrangement #1 would be \"orttu\" and #60 would be \"uttro\".\r\n" );
document.write( "\r\n" );
document.write( "Therefore \"tutor\" would be much closer to the bottom of the list than\r\n" );
document.write( "to the top.  So it will be easier to start at the bottom of the list\r\n" );
document.write( "and go upward to find \"tutor\" than to start at the top and go downward \r\n" );
document.write( "to it.  \r\n" );
document.write( "\r\n" );
document.write( "The last arrangements in the list begin with \"u\".\r\n" );
document.write( "\r\n" );
document.write( "Now we find out the number of  arrangements at the bottom of the list begin with\r\n" );
document.write( "\"u\".  In each of those, the \"u\" is followed by a distinct arrangement of the\r\n" );
document.write( "letters \"o\",\"r\",\"t\",\"t\", of which there are . So the last 12\r\n" );
document.write( "arrangements begin with \"u\", so these 12 arrangements:\r\n" );
document.write( "\r\n" );
document.write( "#60,#59,#58,$57,#56,#55,#54,#53,#52,#51,#50, and #49, all begin with \"u\".\r\n" );
document.write( "\r\n" );
document.write( "The ones just above those 12 in the list begin with \"t\".  The last one that\r\n" );
document.write( "begins with \"t\" is \"tutro\", which is #48, and \"tutor\" is the arrangement just\r\n" );
document.write( "before that.  Therefore \"tutor\" is #47 in the list.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );