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Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.
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Total number of points $=18$
Out of which 5 points are collinear also a straight line is formed by joining any two points
$\therefore$ Number of straight line formed by joining the 18 points taking 2 at a time $={ }^{18} C_2$
Now, 5 points are collinear
$\therefore$ number of straight line formed by joining 5 points taking 2 at a time $={ }^5 C_2$
Also 5 collinear points, when joined pwerwise give only one line
$\therefore$ Required number of straight line
$={ }^{18} C_2-{ }^5 C_2+1=153-10+1=144$
Out of which 5 points are collinear also a straight line is formed by joining any two points
$\therefore$ Number of straight line formed by joining the 18 points taking 2 at a time $={ }^{18} C_2$
Now, 5 points are collinear
$\therefore$ number of straight line formed by joining 5 points taking 2 at a time $={ }^5 C_2$
Also 5 collinear points, when joined pwerwise give only one line
$\therefore$ Required number of straight line
$={ }^{18} C_2-{ }^5 C_2+1=153-10+1=144$
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