document.write( "Question 1155819: How many distinct permutations can be formed using the letters of the word \"CHARACTER\"? \n" ); document.write( "

Algebra.Com's Answer #778498 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "How many $\"highlight%28cross%28distinct%29%29%29\"$ $\"highlight%28cross%28permutations%29%29\"$ distinguishable arrangements can be formed using the letters of the word \"CHARACTER\"?
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document.write( "In all, there are 9 letters in the word.\r\n" );
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document.write( "Of them, letter \"C\" has multiplicity 2;\r\n" );
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document.write( "         letter \"A\" has multiplicity 2;\r\n" );
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document.write( "         letter \"R\" has multiplicity 2.\r\n" );
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document.write( "The rest of the letters are UNIQUE.\r\n" );
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document.write( "The number of distinguishable arrangements of letters is   =  = 45360.    ANSWER\r\n" );
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document.write( "Three times repeated factor 2! in the denominator is to account for three repeated letters \"C\", \"A\" and \"R\" with their multiplicities.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard method of solving such problems and a standard mantra to pronounce.\r
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\n" ); document.write( "\n" ); document.write( "Memorize it (!)\r
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\n" ); document.write( "\n" ); document.write( "To see other similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Arranging elements of sets containing indistinguishable elements \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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