document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183995>Question 1183995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Valentina, Luke, Sally, Han and Mae are to be placed in a line in random order.\r<BR>\n" );
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document.write( "What is the probability that the boys will be next to each other and the girls will all be 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 #814522 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the possible arrangements, without any restrictions, are 5! = 120.<BR>\n" );
document.write( "if the boys need to be together, that can happen in 3! arrangements = 6.<BR>\n" );
document.write( "if the girls need to be together, that can happen in 2! arrangements = 2.<BR>\n" );
document.write( "that would be a total of 6 * 2 = 12 possible arrangements if all the boys are on the left and another total of 2 * 6 = 12 possible arrangements if all the girls are on the left.<BR>\n" );
document.write( "you get 24 possible arrangements out of 120 possible arrangements, giving you a probability of 24/120 = 1/5.\r<BR>\n" );
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document.write( "let the boys be 1,2,3.<BR>\n" );
document.write( "let the girls be a,b.\r<BR>\n" );
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document.write( "when the girls are on the left, you get:\r<BR>\n" );
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document.write( "ab123<BR>\n" );
document.write( "ab132<BR>\n" );
document.write( "ab213<BR>\n" );
document.write( "ab231<BR>\n" );
document.write( "ab312<BR>\n" );
document.write( "ab321\r<BR>\n" );
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document.write( "ba123<BR>\n" );
document.write( "ba132<BR>\n" );
document.write( "ba213<BR>\n" );
document.write( "ba231<BR>\n" );
document.write( "ba312<BR>\n" );
document.write( "ba321\r<BR>\n" );
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document.write( "that's a total of 12.\r<BR>\n" );
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document.write( "when boys are on the left and the girls are on the right, that's another 12 possible arrangements, for a total of 24 out of 120 = 1/5.\r<BR>\n" );
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document.write( "as far as i can tell, the probability is 1/5.\r<BR>\n" );
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