document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=410825>Question 410825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of combinations of 2 objects from 'n' is equal to the number of combinations of 3 objects from 'n'. Determine 'n'. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288814 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=288814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nC2+=+nC3 ALIGN=MIDDLE  ALT=\"nC2+=+nC3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Two ways to solve it:\r<BR>\n" );
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document.write( "Solution 1 (faster solution):<BR>\n" );
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document.write( "If you know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nCk+=+nC%28n-k%29 ALIGN=MIDDLE  ALT=\"nCk+=+nC%28n-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can set k = 2 and n-k = 3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+%2B+%28n-k%29+=+2+%2B+3+=+5 ALIGN=MIDDLE  ALT=\"k+%2B+%28n-k%29+=+2+%2B+3+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so n = 5.\r<BR>\n" );
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document.write( "Solution 2 (algebraic solution):<BR>\n" );
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document.write( "We can write it as an algebraic equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28%28n-2%29%212%21%29+=+n%21%2F%28%28n-3%29%213%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28%28n-2%29%212%21%29+=+n%21%2F%28%28n-3%29%213%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is equivalent to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n-1%29%2F2%21+=+n%28n-1%29%28n-2%29%2F3%21 ALIGN=MIDDLE  ALT=\"n%28n-1%29%2F2%21+=+n%28n-1%29%28n-2%29%2F3%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%21+=+%28n-2%29%2F3%21 ALIGN=MIDDLE  ALT=\"1%2F2%21+=+%28n-2%29%2F3%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+=+%28n-2%29%2F6 ALIGN=MIDDLE  ALT=\"1%2F2+=+%28n-2%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> Cross-multiplying, we get n = 5. </SPAN>\n" );
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