CF528E Triangles 3000
Description
You are given a set $ L={l_{1},l_{2},...,l_{n}} $ of $ n $ pairwise non-parallel lines on the Euclidean plane. The $ i $ -th line is given by an equation in the form of $ a_{i}x+b_{i}y=c_{i} $ . $ L $ doesn't contain three lines coming through the same point.
A subset of three distinct lines is chosen equiprobably. Determine the expected value of the area of the triangle formed by the three lines.
Input Format
N/A
Output Format
N/A
Explanation/Hint
A sample from the statement is shown below. There are four triangles on the plane, their areas are $ 0.25,0.5,2,2.25 $ .
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