There are n≥4 points situated on a plane such that no two of the lines joining them are parallel and no three of the lines joining them are concurrent except at the given points. Find the number of points of intersection, other than the given points, of the lines obtained by joining them.
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2 Answers
62no of ways to select 2 lines not meeting at one of the original points =
nC2x(n-2)C2/ 2
= (n)(n-1)(n-2)(n-3)/8
for each of these, we have 1 point of intersectin..
hence this should be the answer?
62There is another way to look at it
first select 4 point
nC4
for each of these, there will be 3 points of intersection (why?)
thus
3.nC4
which is same as the above answer
