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There are 12 points in plane out of which 5 points are collinear. How many different lines can be drawn using these points?

$\begin{array}{1 1} 66 \\ 65 \\ 57 \\ 56 \end{array}$

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No. of points $=12$
To draw a line two points are required.
If no three points are collinear then the no. of lines = $^{12}C_2$
Since 5 points are collinear, using these 5 points we can draw only one line.
$\therefore$ The no. of different lines $=^{12}C_2-^5C_2+1$ (single line using collinear points)
$=66-10+1=57$
answered Aug 12, 2013 by rvidyagovindarajan_1
 

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