document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835852>Question 835852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Regular polygon has 20 sides. How many triangles can be formed using these vertices but,not using the sides? <BR>\n" );
document.write( "Ans.800 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503789 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=503789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 20C3 = 1140 ways to choose three vertices that form a triangle.\r<BR>\n" );
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document.write( "Of these, there are 20 triangles with two side lengths on the perimeter of the regular polygon. Also, for each side, there are 16 points that can make a triangle with exactly one side length on the 20-gon. This makes <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?20 + 16 \cdot 20 = 340\"> triangles we have to subtract, since one of the side lengths is on the 20-gon.\r<BR>\n" );
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document.write( "1140 - 340 = 800. </SPAN>\n" );
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