document.write( "Question 1143786: what is the permutations of the letters in the word of ASSASSIN? \n" ); document.write( "
Algebra.Com's Answer #764702 by ikleyn(52786)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "what is the permutations of the letters in the word of ASSASSIN?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            The original formulation in the post is INCORRECT.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            The correct formulation is THIS :\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "                What is the number of all distinguishable arrangements of the letters in the word ASSASSIN ?\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "SOLUTION\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The given word has 8 symbols.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of these 8 symbols, the letter \"A\" repeats 2 times, and the letter \"S\" repeats 4 times.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "All other letters are distinct and unique.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of all permutations of 8 symbols is 8!\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But the number of all distinguishable arrangements is  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    8!/(2!*4!) = \"%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29%2F%282%2A24%29\" = 840.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the formula,  2!  in the denominator stands to account for repeating letter \"A\", \r\n" );
document.write( "\r\n" );
document.write( "           while 4! in the denominator stands to account for repeating letter \"S\".\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );