document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113347>Question 1113347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in How many ways can 5 girls any 5 boys be arranged in a row such that the 2 boys are not together.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728366 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52792)</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=728366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "I do not understand why other tutor has some/any doubts.\r<BR>\n" );
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document.write( "There is one and only one reasonable way to read/(to interpret) the condition: \" . . . such that NO two boys are sitting together\".\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "In this problem, you can assume that all the \"seats\" are numbered from 1 to 10, from left to right. \r\n" );
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document.write( "Then, under given conditions, there are only TWO major configurations:\r\n" );
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document.write( "    a)  the boys are placed at the \"odd\" seats;   and/or\r\n" );
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document.write( "    b)  the boys are placed at the \"even\" seats.\r\n" );
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document.write( "Case a) gives  5! = 120 different arrangements for boys and the same number of 5! = 120 different arrangements for girls.\r\n" );
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document.write( "In all, there are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%5E2 ALIGN=MIDDLE  ALT=\"120%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  arrangements, when the boys are seating at  \"odd\" seats.\r\n" );
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document.write( "Case b) gives  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%5E2 ALIGN=MIDDLE  ALT=\"120%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  different arrangements, too (by the same arguments).\r\n" );
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document.write( "Hence, there are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A120%5E2 ALIGN=MIDDLE  ALT=\"2%2A120%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  arrangements, in all.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "On permutations, see the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Problems on Permutations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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