document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207518>Question 1207518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 9 combination n : 8combination (n-2) = 9:4, find the values of n. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845437 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%289%2Cn%29%2FC%288%2C%28n-2%29%29=9%2F4 ALIGN=MIDDLE  ALT=\"C%289%2Cn%29%2FC%288%2C%28n-2%29%29=9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "\"cross multiply\"<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2AC%289%2Cn%29=9%2AC%288%2C%28n-2%29%29 ALIGN=MIDDLE  ALT=\"4%2AC%289%2Cn%29=9%2AC%288%2C%28n-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Rewrite using definition of C(n,r), and simplify<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28%289%21%29%2F%28%28n%21%29%289-n%29%21%29%29=9%2A%28%288%21%29%2F%28n-2%29%21%288-%28n-2%29%29%21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28%289%21%29%2F%28%28n%21%29%289-n%29%21%29%29=9%2A%28%288%21%29%2F%28n-2%29%21%2810-n%29%21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Rearrange factors so that each fraction has \"similar\" factorials<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F9%29%289%21%2F%288%21%29%29=%28%28n%21%29%289-n%29%21%29%2F%28%28n-2%29%21%2810-n%29%21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Simplify and solve<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F9%29%289%29=%28n%28n-1%29%29%2F%2810-n%29 ALIGN=MIDDLE  ALT=\"%284%2F9%29%289%29=%28n%28n-1%29%29%2F%2810-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=%28n%5E2-n%29%2F%2810-n%29 ALIGN=MIDDLE  ALT=\"4=%28n%5E2-n%29%2F%2810-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2810-n%29=n%5E2-n ALIGN=MIDDLE  ALT=\"4%2810-n%29=n%5E2-n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40-4n=n%5E2-n ALIGN=MIDDLE  ALT=\"40-4n=n%5E2-n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B3n-40=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B3n-40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B8%29%28n-5%29=0 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%28n-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "n = -8  or  n = 5<br><BR>\n" );
document.write( "Ignore the negative solution which makes no sense.<br><BR>\n" );
document.write( "ANSWER: n=5<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "C(9,n)=C(9,5)=126<BR>\n" );
document.write( "C(8,n-2)=C(8,3)=56<BR>\n" );
document.write( "126/56=9/4<br><BR>\n" );
document.write( "---------------------------------------------------------<br><BR>\n" );
document.write( "Or, for a faster solution which gives you no practice with manipulating factorials....<br><BR>\n" );
document.write( "n=3? C(9,3)=84; C(8,1)=8; 84/8 not = 9/4 No<BR>\n" );
document.write( "n=4? C(9,4)=126; C(8,2)=28; 126/28 not = 9/4 No<BR>\n" );
document.write( "n=5? C(9,5)=126; C(8,3)=56; 126/56 = 9/4 YES<br><BR>\n" );
document.write( " </SPAN>\n" );
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