document.write( "Question 1134223: In how many ways can 6 people be arranged so that they form a circle between them; and if 2 particular people of the 6 people quarell, how many arrangements must be made if the quarellsome pair must not stand next to each other? \n" ); document.write( "

Algebra.Com's Answer #751566 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "(a) In how many ways can 6 people be arranged so that they form a circle between them;
\n" ); document.write( "(b) and if 2 particular people of the 6 people quarrel, how many arrangements must be made if the quarrelsome pair
\n" ); document.write( "must not stand next to each other?
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\n" ); document.write( "\n" ); document.write( " Pay attention on how I edited your post to separate and clearly show that there are TWO QUESTIONS here.\r
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document.write( "(a)  There are   = (n-1)!  circular arrangements of n objects.\r\n" );
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document.write( "     In this case n = 6, so there are (6-1)! = 5! = 120 circular arrangements of 6 persons.\r\n" );
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document.write( "(b)  Among these 120 circular arrangements, there are ONLY TWO, where the opponents are neighbors. \r\n" );
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document.write( "    So, the answer to question (b) is  120 - 2 = 118 circular arrangements.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On circular arrangements, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Persons sitting around a cicular table \r
\n" ); document.write( "\n" ); document.write( "in this site.\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( "\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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