Question

there are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent determine the number of points of intersection up​

Answer 1

The number of points of intersection up​ is 190.

Step-by-step explanation:

Given,

no 2 lines are parallel, any 2 lines will intersect each other at 1 point.

Also,

∵  no 3 lines are concurrent, no 3 or more lines will intersect at a single point.

∴ The total number of intersection points can be found out by finding the number of combinations of 2 lines.

= $20C_2$

= $\dfrac{20!}{2!(20-2)!}$

=  $\dfrac{20!}{2!18!}$

= $\dfrac{20\times 19\times18!}{2!18!}$

= $\dfrac{20\times 19}{2}$

= 190

Hence, the number of points of intersection up​ is 190.

Answer 2

Step-by-step explanation:

here is your answer^_^