document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=647599>Question 647599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many ways can 7 people A,B,C,D,E,F and G, sit in a row at a movie theater if A and B must sit by each other? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406316 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"if A and B must sit by each other\", then A and B can be thought of as the same person. Think of this person as AB.\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "A,B,C,D,E,F and G\r<BR>\n" );
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document.write( "becomes\r<BR>\n" );
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document.write( "AB,C,D,E,F and G\r<BR>\n" );
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document.write( "So you now have 7-1 = 6 people filling 6 seats. So there are 6! = 720 different ways to fill these seats.\r<BR>\n" );
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document.write( "This is also true for BA. So we double the count to 1440\r<BR>\n" );
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document.write( "Therefore, there are 1440 different ways to seat 7 people where A and B must sit by each other. </SPAN>\n" );
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