document.write( "Question 1178588: five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if\r
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Algebra.Com's Answer #807897 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "(a)  Considering five couples as five special objects,\r\n" );
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document.write( "     we have 5! = 5*4*3*2*1 = 120 permutations of these objects.\r\n" );
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document.write( "     Next, we have 2 possible permutations (A,B) --> (B,A)  inside each of 5 pairs.\r\n" );
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document.write( "     These permutations are independent ---  so, there are   = 32*120 = 3840 permutations of 5 couples, satisfying the imposed conditions.\r\n" );
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document.write( "(b)  If no restrictions are imposed, then there are 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 possible permutations of 10 persons.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On Permutations, see introductory lessons \r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Permutations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Permutations\r
\n" ); document.write( "\n" ); document.write( "    - Simple and simplest problems on permutations\r
\n" ); document.write( "\n" ); document.write( "    - Special type permutations problems \r
\n" ); document.write( "\n" ); document.write( "    - Problems on Permutations with restrictions \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Permutations and Combinations\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 lessons are 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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