There are n 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
There are n 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
The correct options are
C
D 
Since no two lines are parallel and no three are concurrent, therefore n straight lines intersect at nC2 = N (say) points. Since two points are required to determine a straight line, therefore the total number of lines obtained by joining N points NC2. But in this each old line has been counted n−1C2 times, since on each old line there will be n-1 points of intersection made by the remaining (n-1) lines.
Hence the required number of fresh lines is NC2−n.n−1C2 = N(N−1)2−n(n−1)(n−2)2
= nC2(nC2−1)2−n(n−1)(n−2)2 = n(n−1)(n−2)(n−3)8
C
D
Since no two lines are parallel and no three are concurrent, therefore n straight lines intersect at nC2 = N (say) points. Since two points are required to determine a straight line, therefore the total number of lines obtained by joining N points NC2. But in this each old line has been counted n−1C2 times, since on each old line there will be n-1 points of intersection made by the remaining (n-1) lines.
Hence the required number of fresh lines is NC2−n.n−1C2 = N(N−1)2−n(n−1)(n−2)2
= nC2(nC2−1)2−n(n−1)(n−2)2 = n(n−1)(n−2)(n−3)8