document.write( "Question 1193015: 1.Suppose you have n points, no three of which are collinear. How many lines contain two of these n points?\r
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Algebra.Com's Answer #824984 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "1.Suppose you have n points, no three of which are collinear. How many lines contain two of these n points?\r
\n" ); document.write( "\n" ); document.write( "2.If no four of the n points are coplanar, how many planes contain three of the n points?
\n" ); document.write( "Hint: (for 1 and 2, generalize in a form of a formula)
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document.write( "(1)  The number of lines is the number of combinations n points taken 2 at a time\r\n" );
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document.write( "          = .\r\n" );
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document.write( "     Each pair of points determines a unique line.\r\n" );
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document.write( "     For example,  for 4 points  (n = 4),  there are   =  =  = 2*3 = 6 lines.\r\n" );
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document.write( "     Compare it with 4 sides + 2 diagonals of an arbitrary quadrilateral \r\n" );
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document.write( "(2)  The number of planes is the number of combinations of n points taken 3 at a time\r\n" );
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document.write( "          = .\r\n" );
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document.write( "     Each triple of points determines a unique plane.\r\n" );
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document.write( "     For example,  for 4 points  (n = 4),  there are   =  = 4 planes.\r\n" );
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document.write( "     Compare it with 4 faces of a tetrahedron.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
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