document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=427273>Question 427273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the value of r if c(18,r)=c(18,r+2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297128 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=297128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula is:\r<BR>\n" );
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document.write( "c(n,r) = n! / (r! * (n-r)!)\r<BR>\n" );
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document.write( "the numerator will always be the same.\r<BR>\n" );
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document.write( "the denominator also has to be the same.\r<BR>\n" );
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document.write( "in order for this to happen, then r! and (n-r)! have to be reversed.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "1! * 17! = 17! * 1!\r<BR>\n" );
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document.write( "on the left side of the equation, r = 1 and n-r = 17<BR>\n" );
document.write( "on the right sides of the equation, r = 17 and n-r = 1\r<BR>\n" );
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document.write( "you will get 1! * 17! = 17! * 1! yielding the same denominator.\r<BR>\n" );
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document.write( "the difference between the 2, however, is not equal to 2.\r<BR>\n" );
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document.write( "when r and n-r get closer together, the difference will be 2.\r<BR>\n" );
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document.write( "if we pick 8 as r, then n-r becomes 10.\r<BR>\n" );
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document.write( "reversing them, we get r = 10 and n-r = 8.\r<BR>\n" );
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document.write( "this satisfies the condition we are looking for so the answer will be r = 8.\r<BR>\n" );
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document.write( "with r = 8, the formula becomes c(18,8)<BR>\n" );
document.write( "with r = 10, the formula becomes c(18,10)\r<BR>\n" );
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document.write( "c(18,8) = 18! / (8! * 10!)<BR>\n" );
document.write( "c(18,10) = 18! / (10! * 8!)\r<BR>\n" );
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document.write( "the numerator is always the same.<BR>\n" );
document.write( "the denominator is the same as well, only commuted.\r<BR>\n" );
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document.write( "a*b = b*a is the basic commutative property which is why i say the denominator is commuted.\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "r = 8.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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