document.write( "Question 1110776: find the number of distinguishable permutations that can be made from the letters of the word ANTARCTICA \n" ); document.write( "

Algebra.Com's Answer #725772 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "There are 10 letters (symbols) in the word, in all.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of them, there are \r\n" );
document.write( "\r\n" );
document.write( "    - 3 repeating (identical) \"A\", \r\n" );
document.write( "\r\n" );
document.write( "    - 2 repeating (identical) \"T\".\r\n" );
document.write( "\r\n" );
document.write( "    - 2 repeating (identical) \"C\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of distinguishable permutations is  P  =  = 151200.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3! in the denominator accounts for repeating \"A\",\r\n" );
document.write( "\r\n" );
document.write( "2! in the denominator accounts for repeating \"T\",\r\n" );
document.write( "\r\n" );
document.write( "3! in the denominator accounts for repeating \"C\".\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Arranging elements of sets containing indistinguishable elements \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );