Question

If there are n lines passing through a plane, such that no two lines are parallel, how many point of intersection will be there between the lines?

Answer 1

There are `(n(n-1))/2` points of intersection will be there between the `n` lines, when no two lines are parallel.

Explanation:

We have `n` lines and as none of them are parallel,

every pair of lines intersects in exactly one point.

How many ways can we select two lines out of `n` lines?

It is exactly `color(white)x^nC_2`, which is nothing but

`(n(n-1))/2`

Hence, there are `(n(n-1))/2` points of intersection will be there between the `n` lines, when no two lines are parallel.

However, this will be true only if not more than two lines pass through each point. For example, if three lines pass through same point, (none of them parallel), this will not hold and given assumptions stated in the question, `(n(n-1))/2` is the maximum number of points of intersection, that could be there.