document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154621>Question 154621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hey, i would greatly appreciate it if you could solve this combinatorics problem for me\r<BR>\n" );
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document.write( "(n+2)!/n! = 56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113858 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=113858\">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 \frac{\left(n+2\right)!}{n!}=56\"> Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\left(n+2\right)\left(n+2-1\right)\left(n+2-2\right)\left(n+2-3\right)\cdots\left(3\right)\left(2\right)\left(1\right)}{n!}=56\"> Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%21 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how each successive term is going down by 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\left(n+2\right)\left(n+2-1\right)\left(n+2-2\right)\left(n+2-3\right)\left(n+2-4\right)\left(n+2-5\right)\left(n+2-6\right)\cdots\left(3\right)\left(2\right)\left(1\right)}{n\left(n-1\right)\left(n-2\right)\left(n-3\right)\left(n-4\right)\cdots\left(3\right)\left(2\right)\left(1\right)}=56\"> Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21 ALIGN=MIDDLE  ALT=\"n%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 \frac{\left(n+2\right)\left(n+1\right)\left(n\right)\left(n-1\right)\left(n-2\right)\left(n-3\right)\left(n-4\right)\cdots\left(3\right)\left(2\right)\left(1\right)}{n\left(n-1\right)\left(n-2\right)\left(n-3\right)\left(n-4\right)\cdots\left(3\right)\left(2\right)\left(1\right)}=56\"> Subtract and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/combinatorics.png\" alt=\"Photobucket - Video and Image Hosting\">  Cancel out the common terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\left(n+2\right)\left(n+1\right)}{1}=56\"> Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%28n%2B1%29=56 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%28n%2B1%29=56\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B3n%2B2=56 ALIGN=MIDDLE  ALT=\"n%5E2%2B3n%2B2=56\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B3n-54=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B3n-54=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 56 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B9%29%28n-6%29=0 ALIGN=MIDDLE  ALT=\"%28n%2B9%29%28n-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B9=0 ALIGN=MIDDLE  ALT=\"n%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-6=0 ALIGN=MIDDLE  ALT=\"n-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set each factor equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-9 ALIGN=MIDDLE  ALT=\"n=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" > Solve for \"n\"\r<BR>\n" );
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document.write( "So the possible solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-9 ALIGN=MIDDLE  ALT=\"n=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" >. However, you cannot evaluate the factorial of a negative number (well not yet anyway). So the only solution is <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;\" >\r<BR>\n" );
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