document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768428>Question 768428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can 7 people be seated at a round table if 2 particular people must not sit next to each other?\r<BR>\n" );
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document.write( "I need an explanatory answer. <BR>\n" );
document.write( "Thank you! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468358 by </B><A HREF=/tutors/aboutme.mpl?userid=abdullahkhawer><B>abdullahkhawer(5)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=abdullahkhawer><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=abdullahkhawer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 7 People: Person 1, Person 2, 3,4,5,6, and 7<BR>\n" );
document.write( "at a round table<BR>\n" );
document.write( "7 Chairs: 1,2,3,4,5,6,7\r<BR>\n" );
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document.write( "Let chairs 1 and 2 be next to each other; <BR>\n" );
document.write( "Person 1 is at chair 1 and Person 2 is at chair 2<BR>\n" );
document.write( "The rest of the people on 3,4,5,6,7 - can sit in 5! ways\r<BR>\n" );
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document.write( "Next, Person 1 and Person 2 change their positions; <BR>\n" );
document.write( "Person 1 is sitting at 2 and Person 2 is sitting at 1<BR>\n" );
document.write( "The rest of the people on 3,4,5,6,7 - can be rearranged in 5! ways\r<BR>\n" );
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document.write( "Therefore, total number of ways in which Person 1 and Person 2 are next to each other is: 2*5! = 120*2 = 240\r<BR>\n" );
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document.write( "You then have to find in how many ways they are not sitting next to each other; subtract 240 from the total number of possible arrangements;\r<BR>\n" );
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document.write( "In circular permutation, <BR>\n" );
document.write( "Total number of arrangements of n people = (n-1)!<BR>\n" );
document.write( "Here the number of people is 7<BR>\n" );
document.write( "Arrangement = (7-1)! = 6!= 720\r<BR>\n" );
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document.write( "Number of ways Person 1 and Person 2 are not next to each other = 720-240 = 480 </SPAN>\n" );
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