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  4. Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is

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Q. Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is

EAMCETEAMCET 2014

Solution:

Total number of points in a plane is $30 $.
Out of them, $8$ points are collinear.
$\therefore $ Total number of straight lines formed
$={ }^{30} C_{2}-{ }^{8} C_{2}+1 $
$=\frac{30 \times 29}{2}-\frac{8 \times 7}{2 \times 1}+1 $
$=435-28+1=408$