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

Total number of straight lines formed by

$10$ points $={}^{10}{C}_2=\frac{10}{2}\times \frac{9}{1}=45$

Number of straight lines formed by joining the $4$ points $={}^4{C}_2=\frac{4}{2}\times \frac{3}{1}=6$

But, when $4$ collinear points are joined pairwise, they give only one line.

So, required number of straight lines

$=45-6+1=40$

Hence, the number of straight lines is $40$