document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166109>Question 166109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different seating arrangements are possible for 6 people in 4 chairs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122392 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=122392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Since order does not matter (ie the seats have no unique positions), we must use the <a  rel=nofollow HREF=http://www.mathwords.com/c/combination_formula.htm>combination formula</a>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{r}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-r%29%21r%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-r%29%21r%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the combination formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%21%2F%286-4%29%214%21 ALIGN=MIDDLE  ALT=\"6%21%2F%286-4%29%214%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=6 ALIGN=MIDDLE  ALT=\"n=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%21%2F2%214%21 ALIGN=MIDDLE  ALT=\"6%21%2F2%214%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-4 ALIGN=MIDDLE  ALT=\"6-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 2\r<BR>\n" );
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document.write( "Expand 6!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A5%2A4%2A3%2A2%2A1%29%2F2%214%21 ALIGN=MIDDLE  ALT=\"%286%2A5%2A4%2A3%2A2%2A1%29%2F2%214%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand 2!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A5%2A4%2A3%2A2%2A1%29%2F%282%2A1%294%21 ALIGN=MIDDLE  ALT=\"%286%2A5%2A4%2A3%2A2%2A1%29%2F%282%2A1%294%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A5%2A4%2A3%2Across%282%2A1%29%29%2F%28cross%282%2A1%29%294%21 ALIGN=MIDDLE  ALT=\"%286%2A5%2A4%2A3%2Across%282%2A1%29%29%2F%28cross%282%2A1%29%294%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A5%2A4%2A3%29%2F4%21 ALIGN=MIDDLE  ALT=\"%286%2A5%2A4%2A3%29%2F4%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
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document.write( "Expand 4!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A5%2A4%2A3%29%2F%284%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%286%2A5%2A4%2A3%29%2F%284%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F%284%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"360%2F%284%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 6*5*4*3 to get 360\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F24 ALIGN=MIDDLE  ALT=\"360%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 4*3*2*1 to get 24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{6}C_{4}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide\r<BR>\n" );
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document.write( "So 6 choose 4 (where order doesn't matter) yields 15 unique combinations. So there are 15 possible ways that 6 people can sit in 4 chairs.<BR>\n" );
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