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 $\frac{1}{8} n (n - 1) (n - 2) (n - 3)$

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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

\frac{1}{8} n (n - 1) (n - 2) (n - 3)

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Question Text

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

\frac{1}{8} n (n - 1) (n - 2) (n - 3)

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 $\frac{1}{8} n (n - 1) (n - 2) (n - 3)$

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Practice questions from similar books

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 81​n(n−1)(n−2)(n−3)

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Practice questions from similar books

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 $\frac{1}{8} n (n - 1) (n - 2) (n - 3)$