document.write( "Question 1176491: How many distinguishable permutations are possible with all the letters of the word ELLIPSES? \n" ); document.write( "

Algebra.Com's Answer #803549 by MathLover1(20849) $\"\"$ $\"About$

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ELLIPSES has $\"8\"$ letters, $\"2\"$ $\"Es\"$ , $\"2\"$ $\"Ls\"$ , and $\"2\"$ $\"+S\"$ , $\"1\"$ $\"I\"$ , and $\"1\"$ $\"P\"$ \r
\n" ); document.write( "\n" ); document.write( "The formula for indistinguishable permutation is\r
\n" ); document.write( "\n" ); document.write( "n!/(n[1]!n[2]!.....n[k]!)\r
\n" ); document.write( "\n" ); document.write( "where $\"n\"$ is the total number of objects and are the number of indistinguishable objects.\r
\n" ); document.write( "\n" ); document.write( "We have $\"2Es\"$ , $\"2Ls\"$ , and $\"2S\"$ ( $\"1\"$ $\"I\"$ , and $\"1\"$ $\"P\"$ will not make any difference); the formula then becomes:\r
\n" ); document.write( "\n" ); document.write( " $\"8%21%2F%282%212%212%21%29\"$ \r
\n" ); document.write( "\n" ); document.write( "= $\"%288%2A7%2A6%2A5%2A4%2A3%2A2%29%2F%282%2A2%2A2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "=

\r
\n" ); document.write( "\n" ); document.write( "= $\"8%2A7%2A3%2A5%2A2%2A3\"$ \r
\n" ); document.write( "\n" ); document.write( "= $\"5040\"$ \r
\n" ); document.write( "\n" ); document.write( "There are $\"5040\"$ distinguishable permutations of the word $\"ELLIPSES\"$ .\r
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