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There are n straight lines in a plane in...

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)`

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To solve the problem, we need to determine the number of fresh lines introduced by joining the points of intersection of `n` straight lines in a plane, where no two lines are parallel and no three lines meet at a single point. ### Step-by-Step Solution: 1. **Understanding the Problem**: We have `n` lines in a plane. Since no two lines are parallel, every pair of lines will intersect at a unique point. Since no three lines intersect at a single point, each intersection is distinct. 2. **Finding the Number of Intersection Points**: ...
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