Probability Doubt

[Xiang]

please give the logic behind solving. I got the answer but I am not too sure if i have been thinking right.

THERE ARE 12 POINTS IN A PLANE OF WHICH 5 ARE COLLINEAR. HOW MANY LINES CAN BE CONSTRUCTED BY JOINING 2 POINTS?
ALSO, HOW MANY TRIANGLES ARE POSSIBLE.

Thanks :)

[MI]

Number of straight lines = N ( when all points are non-collinear) - N ( multiple counts due to 5 collinear points) + 1  

= 12C2 -5C2 +1

1 for the line containing those 5 collinear points


For triangles = 12C3 - 5C3

5C3  is the number of triangles which were not made due to collinear points

[Xiang]

thank you so much