Six non collinear points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points of intersection is equal to ___________.
Six non collinear points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points of intersection is equal to ___________.
The correct option is C 51
Number of lines from 6 points = 6C2 =15. Points of intersection obtained from these lines =15C2 =105
. Now we find the number of times, the original 6 points come.
Consider one point say A1 . Joining A1 to remaining 5 points, we get 5 lines, and any two lines
from these 5 lines give A1 as the point of intersections.
∴ A1 Come 5C2 =10 times in 105 points of intersections.
Similar is the case with other five points.
∴ 6 original points come 6×10=60 times in points of intersection.
Hence the number of distinct points of intersection =105 - 60 + 6 =51 (6 is added because we also count 6 original points).
51
Number of lines from 6 points = 6C2 =15. Points of intersection obtained from these lines =15C2 =105
. Now we find the number of times, the original 6 points come.
Consider one point say A1 . Joining A1 to remaining 5 points, we get 5 lines, and any two lines
from these 5 lines give A1 as the point of intersections.
∴ A1 Come 5C2 =10 times in 105 points of intersections.
Similar is the case with other five points.
∴ 6 original points come 6×10=60 times in points of intersection.
Hence the number of distinct points of intersection =105 - 60 + 6 =51 (6 is added because we also count 6 original points).
