There are ten points in the plane, no three of which are coolinear. How many different lines can be drawn through these points ?

Explanation

There are ten points `P_(1), P_(2),.., P_(10)`.
For one line two points are required.
Through point `P_(1)` there will be 9 lines when `P_(1)` is joined with any of the nine other points.
Similarly, there will be nine lines passing through each point.
So, number of lines is `9xx10` or 90.
But there is double counting in above answer. Why ?
One of the nine lines passing through point `P_(1) " is" P_(1) P_(2). "But" P_(1) P_(2)` is also one of the lines passing through point `P_(2)`.
Thus, line `P_(1)P_(2)` and similarly each line is counted twice. Therefore, actual number of lines is `(90)/(2)=45`.