the number of lines passing through 5 points such that no three of them are collinear is
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The first point can be joined with 4 other points to get 4 lines. The second point can be joined with 4 points too. But since we have already taken into account the line between point 1 and 2, only 3 new line segments can be formed from point 2. Similarly, 2 new line segments for point 3 and 1 new line segment for point 4. Therefore we end up with a total of 10 line segments.
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