There are 
straight lines in a plane, no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is
Text Solution
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Since no two lines are parallel and no three are concurrent, therefore 
straight lines intersect at 
(say) points. Since two points are required to determine a straight line, therefore the total number of lines obtained by joining 
points 
. But in this each old line has been counted 
times, since on each old line there will be 
points of intersection made by the remaining 
lines.
Hence the required number of fresh lines is
.
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