document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476326>Question 476326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear math teacher, \r<BR>\n" );
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document.write( "I am having difficulties solving for n in the following problem:\r<BR>\n" );
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document.write( "nC12 = nC8<BR>\n" );
document.write( "n!/(n-12)!12! = n!/(n-8)!8!<BR>\n" );
document.write( "n(n-1)...(n-11)(n-12)!/(n-12)!12! = n(n-1)...(n-7)(n-8)!/(n-8)!8!<BR>\n" );
document.write( "(n-8)(n-9)(n-10)(n-11)/12! = 1/8!<BR>\n" );
document.write( "n^4-21n^3+110n^2-17n^3+357n^2-1870n+72n^2-1512n+7920 / 12! = 1/8!\r<BR>\n" );
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document.write( "Would you please let me know whether I am on the right track?  My solving steps seem convoluted like a kidney tubule! Please let me know where I made an error. \r<BR>\n" );
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document.write( "Thank you very much. \r<BR>\n" );
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document.write( "Yours, \r<BR>\n" );
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document.write( "I. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326617 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=326617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you're on the right track, but you needed to do some other type thinking before getting to the solution, which is a rule that i will explain to you after.<BR>\n" );
document.write( "the equation is:<BR>\n" );
document.write( "nC12 = nC8<BR>\n" );
document.write( "this formula translates to:<BR>\n" );
document.write( "n!/(12!*(n-12)!) = n!/(8!*(n-8)!)<BR>\n" );
document.write( "cross multiply to get:<BR>\n" );
document.write( "n! * (8!*(n-8)!) = n! * (12!*(n-12)!)<BR>\n" );
document.write( "divide both sides of this equation by n! to get:<BR>\n" );
document.write( "8! * (n-8)! = 12! * (n-12)!<BR>\n" );
document.write( "divide both sides of this equation by 8! and divide both sides of this equation by (n-8)! to get:<BR>\n" );
document.write( "(n-8)! / (n-12)! = 12!/8!<BR>\n" );
document.write( "12! is equal to 12 * 11 * 10 * 9<BR>\n" );
document.write( "(n-8)! / (-12)! is equal to (n-8)*(n-9)*(n-10)*(n-11)*(n-12)! / (n-12)! which is equal to:<BR>\n" );
document.write( "(n-8)*(n-9)*(n-10)*(n-11)<BR>\n" );
document.write( "our equation becomes:<BR>\n" );
document.write( "(n-8)*(n-9)*(n-10)*(n-11) = 12*11*10*9<BR>\n" );
document.write( "the left side of this equation will be equal to the right side of this equation if:<BR>\n" );
document.write( "n-8 = 12<BR>\n" );
document.write( "n-9 = 11<BR>\n" );
document.write( "n-10 = 10<BR>\n" );
document.write( "n-11 = 9<BR>\n" );
document.write( "all of these equation would be true if n = 20.<BR>\n" );
document.write( "that's your answer.<BR>\n" );
document.write( "n = 20.<BR>\n" );
document.write( "20C12 = 125970<BR>\n" );
document.write( "20C8 = 125970<BR>\n" );
document.write( "they're the same.<BR>\n" );
document.write( "note that 12 + 8 = 20<BR>\n" );
document.write( "that's the rule.<BR>\n" );
document.write( "you can use it with any problems of this type to immediately get the answer.<BR>\n" );
document.write( "an example:<BR>\n" );
document.write( "nC13 = nC22<BR>\n" );
document.write( "13 + 22 = 35<BR>\n" );
document.write( "your answer is n = 35<BR>\n" );
document.write( "35C13 = 1476337800<BR>\n" );
document.write( "35C22 = 1476337800<BR>\n" );
document.write( "The basic properties of combinations allows this to happen.<BR>\n" );
document.write( "that property is that nCx = nC(n-x)<BR>\n" );
document.write( "from that formula, you get x + (n-x) = n<BR>\n" );
document.write( "a simpler example:<BR>\n" );
document.write( "take n = 7<BR>\n" );
document.write( "your values for each of the possible combinations are:<BR>\n" );
document.write( "7C0 = 1<BR>\n" );
document.write( "7C1 = 7<BR>\n" );
document.write( "7C2 = 21<BR>\n" );
document.write( "7C3 = 35<BR>\n" );
document.write( "7C4 = 35<BR>\n" );
document.write( "7C5 = 21<BR>\n" );
document.write( "7C6 = 7<BR>\n" );
document.write( "7C7 = 1<BR>\n" );
document.write( "you can see that 7Cx = 7C(7-x)<BR>\n" );
document.write( "this makes 7C0 = 7C7<BR>\n" );
document.write( "this makes 7C1 = 7C6<BR>\n" );
document.write( "this makes 7C2 = 7C5<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "Add the x and the (n-x) together and you get 7 every time.<BR>\n" );
document.write( "your problem as nC12 = nC8<BR>\n" );
document.write( "add 12 and 8 together and you get 20.<BR>\n" );
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