document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251519>Question 251519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5^C2 + 5^C1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183234 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=183234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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 given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F%285-2%29%212%21 ALIGN=MIDDLE  ALT=\"5%21%2F%285-2%29%212%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   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{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F3%212%21 ALIGN=MIDDLE  ALT=\"5%21%2F3%212%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-2 ALIGN=MIDDLE  ALT=\"5-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2A3%2A2%2A1%29%2F3%212%21 ALIGN=MIDDLE  ALT=\"%285%2A4%2A3%2A2%2A1%29%2F3%212%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand 3!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2A3%2A2%2A1%29%2F%283%2A2%2A1%292%21 ALIGN=MIDDLE  ALT=\"%285%2A4%2A3%2A2%2A1%29%2F%283%2A2%2A1%292%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{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%2A2%2A1%29%292%21 ALIGN=MIDDLE  ALT=\"%285%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%2A2%2A1%29%292%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{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%29%2F2%21 ALIGN=MIDDLE  ALT=\"%285%2A4%29%2F2%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\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{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"%285%2A4%29%2F%282%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{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"20%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 5*4 to get 20\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F2 ALIGN=MIDDLE  ALT=\"20%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2*1 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide\r<BR>\n" );
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document.write( "So 5 choose 2 (where order doesn't matter) yields 10 unique combinations\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 given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F%285-1%29%211%21 ALIGN=MIDDLE  ALT=\"5%21%2F%285-1%29%211%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   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{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F4%211%21 ALIGN=MIDDLE  ALT=\"5%21%2F4%211%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-1 ALIGN=MIDDLE  ALT=\"5-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 4\r<BR>\n" );
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document.write( "Expand 5!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2A3%2A2%2A1%29%2F4%211%21 ALIGN=MIDDLE  ALT=\"%285%2A4%2A3%2A2%2A1%29%2F4%211%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%291%21 ALIGN=MIDDLE  ALT=\"%285%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%291%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{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%291%21 ALIGN=MIDDLE  ALT=\"%285%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%291%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{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2F1%21 ALIGN=MIDDLE  ALT=\"%285%29%2F1%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
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document.write( "Expand 1!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2F%281%29 ALIGN=MIDDLE  ALT=\"%285%29%2F%281%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{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%281%29 ALIGN=MIDDLE  ALT=\"5%2F%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 5 to get 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F1 ALIGN=MIDDLE  ALT=\"5%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 1 to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{1}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide\r<BR>\n" );
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document.write( "So 5 choose 1 (where order doesn't matter) yields 5 unique combinations\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{2}=10\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{1}=5\">, this means <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}C_{2} } + \textrm{_{5}C_{1} } = 10 + 5 = 15\"> </SPAN>\n" );
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