There are 10 points in a plane of which 4 are collinear.

Question:

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Solution:

Number of straight lines formed joining the 10 points, taking 2 points at a time $={ }^{10} C_{2}=\frac{10}{2} \times \frac{9}{1}=45$

Number of straight lines formed joining the 4 points, taking 2 points at a time $={ }^{4} C_{2}=\frac{4}{2} \times \frac{3}{1}=6$

But, when 4 collinear points are joined pair wise, they give only one line.

$\therefore$ Required number of straight lines $=45-6+1=40$

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