document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187221>Question 1187221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If C(n,4)=C(n,10). What is the value 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 #818164 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think it's 14.<BR>\n" );
document.write( "c(14,4) = 1001<BR>\n" );
document.write( "c(14,10) = 1001\r<BR>\n" );
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document.write( "the value of n would be equal to 4 + 10 = 14.\r<BR>\n" );
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document.write( "the formula for c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "when x = 4, the formula becomes c(n,4) = n! / (4! * (n-4)!).\r<BR>\n" );
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document.write( "when x = 10, the formula becomes c(n,10) = n! / (10! * (n-10!)).\r<BR>\n" );
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document.write( "when c(n,4) = c(n,10), the formula becomes n! / (4! * (n-4)!)  = n! / (10! * (n-10)!).\r<BR>\n" );
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document.write( "since n! is in both equations, then, for these to be equal, 4! * (n-4)! must be equal to 10! * (n-10)!.\r<BR>\n" );
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document.write( "these would be equal if (n-4)! = 10! and (n-10)! = 4!.\r<BR>\n" );
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document.write( "you would then get 4! * 10! = 10! * 4!.\r<BR>\n" );
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document.write( "for (n-4)! to be equal to 10!, n-4 must be equal to 10, and for (n-10)! to be equal to 4!, n - 10 must be equal to 4.\r<BR>\n" );
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document.write( "if n - 4 = 10, then n must be equal to 14.<BR>\n" );
document.write( "if n - 10 = 4, then n must be equal to 14.\r<BR>\n" );
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document.write( "it looks like n has to be equal to 14.<BR>\n" );
document.write( "note that 10 + 4 = 14.\r<BR>\n" );
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document.write( "assuming n = 14, you get:\r<BR>\n" );
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document.write( "c(14,4) = 14! / (4! * 10!) and you get c(14,10) = 14! / (10! * 4!).\r<BR>\n" );
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document.write( "when you work them through, you get:\r<BR>\n" );
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document.write( "14! / (4! * 10!) = 1001<BR>\n" );
document.write( "14! / (10! * 4!) = the same.\r<BR>\n" );
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document.write( "your solution is that the value of  n = 14.\r<BR>\n" );
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document.write( "here is the complete set of combination formulas for c(n,x) where n = 14 and x equal 0 to 14.\r<BR>\n" );
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document.write( "as you can see, there is some symmetry in the values.<BR>\n" );
document.write( "c(n,x) is equal to c(n,(n-x)).<BR>\n" );
document.write( "when n = 14 and x = 4, you get:<BR>\n" );
document.write( "c(14,4) is equal to c(14,10).\r<BR>\n" );
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document.write( "another example:<BR>\n" );
document.write( "c(14,3) = 364<BR>\n" );
document.write( "c(14,14-3) = c(14,11) = 364. </SPAN>\n" );
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