document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192269>Question 192269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q: There are 12 points in a plane of which 5 are collinear. The number of triangles is?\r<BR>\n" );
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document.write( "I think we have to combine C(5,2) (out of 5 collinear, 2 points can form a side of triangle) with the combination of the rest of the points... but i m not getting any answer out of the four options<BR>\n" );
document.write( "a)200<BR>\n" );
document.write( "b)211<BR>\n" );
document.write( "c)210<BR>\n" );
document.write( "d)none of these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144800 by </B><A HREF=/tutors/aboutme.mpl?userid=bhayzone><B>bhayzone(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bhayzone><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=144800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think the answer is D - none of the above. I get a total of 105 triangles\r<BR>\n" );
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document.write( "I'm assuming coliner means they are on the same line.\r<BR>\n" );
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document.write( "5 points on the same line (assume they form one side of the triangle). So how many distinct 2 points (as two points constitue one side) can you select from a set of 5 points. Note side AB = Side BA so this is a combination problem.\r<BR>\n" );
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document.write( "5! div 2!*3! = 10 sides -------------- A\r<BR>\n" );
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document.write( "From the Remaining 7 points, how many triangles can you make. This is same as asking you to select 3 distinct points from 7. Again a combination problem as Triangle ABC = Triangle BAC\r<BR>\n" );
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document.write( "7! div 3!*4! = 35 -------------------- B\r<BR>\n" );
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document.write( "NOT DONE YET !!!<BR>\n" );
document.write( "Each side in A can combile with each of the 7 points to make a triangle. Thus, 10 sides can make 70 triangles ----- C\r<BR>\n" );
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document.write( "Answer = C+B = 105<BR>\n" );
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