document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044457>Question 1044457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> nCr:nC(r-1) = 2:3 , nC(r-2):nC(r-1) = 4:3 find n and r\r<BR>\n" );
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document.write( "Could someone solve it for me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659785 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659785\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> nCr=n!/r!(n-r)!<BR>\n" );
document.write( "nC(r-1)=n!/(r-1)!(n-r+1)!, watch the sign there.<BR>\n" );
document.write( "nC(r-2)=n!/(r-2)(n-r+2)!<BR>\n" );
document.write( "-------------------Divide nCr by nC(r-1)<BR>\n" );
document.write( "n!/r!(n-r)!/n!/(r-1)!(n-r+1)!  The n! cancels and you invert the denominator<BR>\n" );
document.write( "(n-r+1)!(r-1)!/r!(n-r)!<BR>\n" );
document.write( "(r-1)!/r!=1/r<BR>\n" );
document.write( "(n-r+1)!/(n-r)!=n-r+1<BR>\n" );
document.write( "The quotient for this is (n-r+1)/r=2/3<BR>\n" );
document.write( "cross-multiply and you get 3n-3r+3=2r<BR>\n" );
document.write( "3n+3=5r<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "now do nC(r-2)/nC(r-1)<BR>\n" );
document.write( "n!/(r-2)!(n-r+2)!/n!/(n-r+1)!<BR>\n" );
document.write( "do the same thing with canceling the n! and inverting the denominator<BR>\n" );
document.write( "get (r-1)!(n-r+1)!/(r-2)!(n-r+2)!<BR>\n" );
document.write( "this is (r-1)/(n-r+2) =4/3<BR>\n" );
document.write( "cross-multiply<BR>\n" );
document.write( "3r-3=4n-4r+8<BR>\n" );
document.write( "7r=4n+11<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "rewrite as<BR>\n" );
document.write( "7r-4n=11<BR>\n" );
document.write( "5r-3n=3<BR>\n" );
document.write( "multiply the top by 3 and the bottom by (-4)<BR>\n" );
document.write( "21r-12n=33<BR>\n" );
document.write( "-20r+12n=-12<BR>\n" );
document.write( "r=21<BR>\n" );
document.write( "substitute and n=34<BR>\n" );
document.write( "34C21, 34C20, 34 C 19<BR>\n" );
document.write( "The first is 927983760, the second is 1391975640, and they are in a 2:3 ratio.  Really!<BR>\n" );
document.write( "The third is 1855967520<BR>\n" );
document.write( "The last divided by the second is 1.3333 repeat, which is 4:3<BR>\n" );
document.write( "n is 34<BR>\n" );
document.write( "r is 21 </SPAN>\n" );
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