document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149900>Question 149900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know where to start with this one.<BR>\n" );
document.write( "It is in a chapter called intro to probability.\r<BR>\n" );
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document.write( "nC8 = nC7   Find N\r<BR>\n" );
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document.write( "the answer is: n=15\r<BR>\n" );
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document.write( "the 2 Ns and the numerals 7 and 8 are all subscripts. <BR>\n" );
document.write( "Ineed to understand the steps involved. I know how to use basic algebra, it is the subscripts I don't know how to deal with.\r<BR>\n" );
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document.write( "thanks in advance for any help. <BR>\n" );
document.write( "Heidi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110005 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=110005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, the combination formula is: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{r}=\frac{n!}{\left(n-r\right)!r!}\">\r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{8}=\frac{n!}{\left(n-8\right)!8!}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{7}=\frac{n!}{\left(n-7\right)!7!}\"> \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{8}=\textrm{_{n}C_{7}\"> becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{n!}{\left(n-8\right)!8!}=\frac{n!}{\left(n-7\right)!7!}\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{\left(n-8\right)!8!}=\frac{1}{\left(n-7\right)!7!}\"> Divide both sides by <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;\" >. Notice how the <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;\" > terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n-7\right)!7!=\left(n-8\right)!8!\"> Cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n-7\right)!(7)(6)(5)(4)(3)(2)(1)=\left(n-8\right)!(8)(7)(6)(5)(4)(3)(2)(1)\"> Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%21 ALIGN=MIDDLE  ALT=\"7%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%286%29%285%29%284%29%283%29%282%29%281%29 ALIGN=MIDDLE  ALT=\"%287%29%286%29%285%29%284%29%283%29%282%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%21 ALIGN=MIDDLE  ALT=\"8%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%287%29%286%29%285%29%284%29%283%29%282%29%281%29 ALIGN=MIDDLE  ALT=\"%288%29%287%29%286%29%285%29%284%29%283%29%282%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how the terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%286%29%285%29%284%29%283%29%282%29%281%29 ALIGN=MIDDLE  ALT=\"%287%29%286%29%285%29%284%29%283%29%282%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n-7\right)!=\left(n-8\right)!(8)\"> Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n-7\right)!=8\left(n-8\right)!\"> Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\left(n-7\right)!}{8\left(n-8\right)!}=1\"> Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28n-8%29%21 ALIGN=MIDDLE  ALT=\"8%28n-8%29%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-7\right)\left(n-8\right)\left(n-9\right)\left(n-10\right)\cdots(3)(2)(1)}{\left(n-8\right)\left(n-9\right)\left(n-10\right)\cdots(3)(2)(1)}=1\"> Expand the factorials\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/canceled17-27-08.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/plot-formula.mpl?expression=%28n-7%29%2F8=1 ALIGN=MIDDLE  ALT=\"%28n-7%29%2F8=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-7=8 ALIGN=MIDDLE  ALT=\"n-7=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 8.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=8%2B7 ALIGN=MIDDLE  ALT=\"n=8%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15 ALIGN=MIDDLE  ALT=\"n=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15 ALIGN=MIDDLE  ALT=\"n=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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