Explanation

(c)
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 remaiming 5 points, we get 5 lines and any two lines from these 5 lines gives $A_{1}$ as the point of intersection.
$\therefore A_{1}$ is commom in $\ ^{5}C_{2} = 10$ times out of 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
$= 105 - 60 + 6 = 51$