document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062718>Question 1062718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4 boys and 2 girls are sitting on a bench<BR>\n" );
document.write( "1) what is the number of possible dispositions<BR>\n" );
document.write( "2) same question if the boys are sitting on a side and the girls are on the other side <BR>\n" );
document.write( "3) same question if each girl is sitting between 2 boys <BR>\n" );
document.write( "4) same question if the 2 girls want to sit 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 #677706 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1)<BR>\n" );
document.write( "There can be a boy or a girl in any position,<BR>\n" );
document.write( "so you can just regard them as people.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2A2%2A3%2A4%2A5%2A6+=+720+ ALIGN=MIDDLE  ALT=\"+1%2A2%2A3%2A4%2A5%2A6+=+720+\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible arrangements<BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "Multiply all possible groupings of boys times<BR>\n" );
document.write( "all possible groupings of girls<BR>\n" );
document.write( "Then times 2, since they can switch sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+1%2A2%2A3%2A4+%29%2A%28+1%2A2+%29%2A2+=+96+ ALIGN=MIDDLE  ALT=\"+%28+1%2A2%2A3%2A4+%29%2A%28+1%2A2+%29%2A2+=+96+\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible seatings<BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "If you line up the 4 boys, there are only 3 ways<BR>\n" );
document.write( "that 2 girls can sit between 4 boys:<BR>\n" );
document.write( "b g b g b b<BR>\n" );
document.write( "b b g b g b<BR>\n" );
document.write( "b g b b g b<BR>\n" );
document.write( "Also, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2A2+=+2+ ALIGN=MIDDLE  ALT=\"+1%2A2+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to seat the girls<BR>\n" );
document.write( "for each of the 3 ways, so I have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A3+=+6+ ALIGN=MIDDLE  ALT=\"+2%2A3+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so far<BR>\n" );
document.write( "The boys can sit in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2A2%2A3%2A4+=+24+ ALIGN=MIDDLE  ALT=\"+1%2A2%2A3%2A4+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" > different ways<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A24+=+144+ ALIGN=MIDDLE  ALT=\"+6%2A24+=+144+\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible seatings<BR>\n" );
document.write( "(4)<BR>\n" );
document.write( "Here are the possible ways that 2 girls can sit next to each other:<BR>\n" );
document.write( "g g b b b b<BR>\n" );
document.write( "b g g b b b <BR>\n" );
document.write( "b b g g b b <BR>\n" );
document.write( "b b b g g b <BR>\n" );
document.write( "b b b b g g <BR>\n" );
document.write( "or, 5 different ways<BR>\n" );
document.write( "The girls can swap positions, so there are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A5+=+10+ ALIGN=MIDDLE  ALT=\"+2%2A5+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways so far<BR>\n" );
document.write( "The boys can still be arranged in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2A2%2A3%2A4+=+24+ ALIGN=MIDDLE  ALT=\"+1%2A2%2A3%2A4+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" > different ways<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2A24+=+240+ ALIGN=MIDDLE  ALT=\"+10%2A24+=+240+\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible seatings<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "It wouldn't hurt to get other opinions, too<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );