document.write( "Question 39270: Using the letters A,M,O,S,U. We can form 120 five letter \"words\". If these \"words\" are arranged in alphabetical order, then what position the \"word\"
\n" ); document.write( "USAMO occupies? \n" ); document.write( "

Algebra.Com's Answer #24719 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I come up with the 115th position in the list.
\n" ); document.write( "The list of 120 words is made up of:
\n" ); document.write( "24 words that start with \"A\"
\n" ); document.write( "24 words that start with \"M\"
\n" ); document.write( "24 words that start with \"O\"
\n" ); document.write( "24 words that start with \"S\"
\n" ); document.write( "24 words that start with \"U\"
\n" ); document.write( "5 X 24 = 120
\n" ); document.write( "\"USAMO\" occurs after 4 X 24 words, or after 96 words on the list
\n" ); document.write( "the 97th word is \"UAMOS\"
\n" ); document.write( "6 X 4 = 24 words that start with \"U\"
\n" ); document.write( "There are 6 words that start with \"US\"
\n" ); document.write( "There are 6 words that start with \"UA\"
\n" ); document.write( "There are 6 words that start with \"UM\"
\n" ); document.write( "There are 6 words that start with \"UO\"
\n" ); document.write( "The first word that starts with \"US\" is \"USAMO\"
\n" ); document.write( "So, the number on the list is:
\n" ); document.write( "96 + (3*6) + 1 = 96 + 19 = 115 \n" ); document.write( "

\n" );