document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175241>Question 1175241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Vanessa plans to arrange A, B, C, D, E, F, G, and H in a row on the wall. Find<BR>\n" );
document.write( "the number of permutations for each of the following.<BR>\n" );
document.write( "1. A and B must be placed next to each other.<BR>\n" );
document.write( "2. A and B must not be placed next to each other.<BR>\n" );
document.write( "3. A, B, and C must be placed next to each other, and at the same time, E,F and G must also be placed next to 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 #800822 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52791)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "I solved part (1) yesterday under this link\r<BR>\n" );
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document.write( "<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1175182.html>https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1175182.html</A>\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1175182.html\r<BR>\n" );
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document.write( "But I agree to reproduce it here &nbsp;AGAIN, &nbsp;because it is closely connected with part &nbsp;(2).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Part (1)</U>\r<BR>\n" );
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document.write( "For the rest of &nbsp;6 &nbsp;letters, &nbsp;C, D, E, F, G and H, &nbsp;there are &nbsp;&nbsp;6! = 720 possible permutations.\r<BR>\n" );
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document.write( "For each of these &nbsp;720 &nbsp;permutations, &nbsp;we have &nbsp;7 &nbsp;positions to place the blocked &nbsp;AB &nbsp;or &nbsp;BA.\r<BR>\n" );
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document.write( "THEREFORE, &nbsp;the full number of possible arrangements, &nbsp;satisfying the posed conditions, is\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6!*2*7 = 2*7! = 10080.      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U><BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Part &nbsp;(2)</U>\r<BR>\n" );
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document.write( "These permutations are &nbsp;COMPLEMENT to  &nbsp;&nbsp;8! = 40320,\r<BR>\n" );
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document.write( "so their number is  &nbsp;&nbsp;40320 - 10080 = 30240.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "I will not solve here part &nbsp;(3), &nbsp;since I think it is &nbsp;TOOOOOO &nbsp;much for one post.\r<BR>\n" );
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document.write( "It is not a way to teach people.\r<BR>\n" );
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document.write( "It is the way to work instead of them and to perform their job, &nbsp;what I do not want to do.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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