If n straight lines in a plane are such that no two of them are parallel and no three of them are concurrent, prove that they intersect each other in `(n(n-1))/2` points.

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent. In how many points will they intersect each other ?

If n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent, such that these lines divide the planein 67 parts, then find number of different points at which these lines will cut.

If n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent, then find number of different points at which these lines will cut.

Six straight lines are in a plane such that no two are parallel & no three are concurrent. The number of parts in which these lines divide the plane will be

There are n straight lines in a plane such that n_(1) of them are parallel in onne direction, n_(2) are parallel in different direction and so on, n_(k) are parallel in another direction such that n_(1)+n_(2)+ . .+n_(k)=n . Also, no three of the given lines meet at a point. prove that the total number of points of intersection is (1)/(2){n^(2)-sum_(r=1)^(k)n_(r)^(2)} .

There are n straight lines in a plane in which no two are parallel and no three pass through the same point. Their points of intersection are joined. Show that the number of fresh lines thus introduced is 1/8n(n-1)(n-2)(n-3)

Two intersecting lines can intersect each other at more than one point.

If m parallel lines in a plane are intersected by a family of n parallel lines, find the number of parallelograms formed.

Two lines, which are both parallel to the same line, are parallel to each other, prove that.

If n objects are arrange in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is