document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476308>Question 476308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear math teacher,\r<BR>\n" );
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document.write( "I am having difficulties with the following problem:\r<BR>\n" );
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document.write( "4 times nC2 = (n+2)C3, (a)solve for n; (b) n cannot equal to or must be different from ...integers.\r<BR>\n" );
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document.write( "4*n(n-1)*(n-2)!/(n-2)!(2.1) = (n+2)!/(n+2-3)!*(3.2.1) and after canceling out 2(n-2)! we get\r<BR>\n" );
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document.write( "2n(n-1) = (n+2)(n+1)n(n-1)!/(n-1)!(3.2.1) and after canceling out n and (n-1)! we get\r<BR>\n" );
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document.write( "2(n-1) = (n+2)(n+1)/6\r<BR>\n" );
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document.write( "n^2 - 9n + 14 = 0<BR>\n" );
document.write( "(n-7)(n-2) = 0<BR>\n" );
document.write( "n=7 and n=2\r<BR>\n" );
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document.write( "To answer part (a) of the problem, I say the solution is 7 only since (n-2) was canceled out above. For part (b) n cannot equal to 0, 1, and 2 since n canceled out, (n-1) canceled out, and (n-2) term canceled out.\r<BR>\n" );
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document.write( "Please let me know, if I reason through this correctly. Thank you very much.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326596 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=326596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you calculated the answer correctly.<BR>\n" );
document.write( "n is equal to 7 or n is equal to 2.<BR>\n" );
document.write( "that takes care of part a.<BR>\n" );
document.write( "both of those values of n will make the equations equal.<BR>\n" );
document.write( "that was confirmed.<BR>\n" );
document.write( "part b says n cannot be equal to, or must be different from ... integers?<BR>\n" );
document.write( "not sure i understand that, but, if i must pick a number that should be disallowed, it would be n = 2.<BR>\n" );
document.write( "your equation is:<BR>\n" );
document.write( "4*nC2 = (n+2)C3<BR>\n" );
document.write( "this equation can be translated to:<BR>\n" );
document.write( "(4*n!)/(2!(n-2)!) = (n+2)!/(3!(n+2-3)!) which becomes:<BR>\n" );
document.write( "(4*n!)/(2!(n-2)!) = (n+2)!/(3!(n-1)!)<BR>\n" );
document.write( "when n = 7, this equation becomes:<BR>\n" );
document.write( "4*7!/(2!*5!) = 9!/(3!*6!)<BR>\n" );
document.write( "when n = 2, this equation becomes:<BR>\n" );
document.write( "4*2!/(2!*0!) = 4!/(3!*1!)<BR>\n" );
document.write( "the left side of this equation have n equal to 2 which is equal to the number of positions in the subgroup you are trying to create.<BR>\n" );
document.write( "if that's what they're referring to, then n = 2 would be disallowed because the subgroup is the same size as the group.<BR>\n" );
document.write( "outside of that I'm not exactly sure what their complaint is.<BR>\n" );
document.write( "assuming i understood correctly, i would say that n = 2 would be disallowed because the group created is the same size as the subgroup that would be created from it.\r<BR>\n" );
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