There are 20 straight lines in a plane such that no two of them are parallel and no three of them are concurrent. If these points of intersection are joined, then the number of new line segments formed are 

Given that there are 20 straight lines that are neither parallel nor three of them are concurrent. 

The number of points of intersections are ${ }^{20}{\mathrm{C}}_2=\frac{20·19}{2}=190$

Since each line intersects the other 19 lines, among the above points there are 19 points on each line because of the other 19 lines.

The number of lines generated by these 19 points is ${ }^{19}{\mathrm{C}}_2=\frac{19·18}{2}=171$, these lines are not new lines

Hence, the total number of new lines is

                $\begin{array}{rcl}{{ }^{190}\mathrm{C}}_2-20·\left(171\right)& =& \frac{190·189}{2}-3420\\ & =& 17955-3420=14535\end{array}$

Hence, the number of new line segments formed is 14535.