A) 105
B) 45
C) 51
D) None of these
Correct Answer: C
Solution :
Number of lines from 6 points\[{{=}^{6}}{{C}_{2}}=15\]. Points of intersection obtained from these lines\[{{=}^{15}}{{C}_{2}}=105\]. Now we find the number of times, the original 6 points come. Consider one point say\[{{A}_{1}}\]. Joining \[{{A}_{1}}\]to remaining 5 points, we get 5 lines, and any two lines from these 5 lines give \[{{A}_{1}}\] as the point of intersection. \[\therefore \]\[{{A}_{1}}\] come\[^{5}{{C}_{2}}=10\] times in 105 points of intersections. Similar is the case with other five points. \[\therefore \] 6 original points come \[6\times 10=60\] times in points of intersection. Hence the number of distinct points of intersection\[=105-60+6=51\].
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