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.

Answer 1

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.
∴ Required number of straight lines = $45-6+1=40$