Question

out of 8 points in a plane 5 are Collinear find the probability that 3 point selected at random from a triangle

Answer 1

Given : 5 points are collinear and 3 points are non-collinear

Aim: Selecting 3 points such that a triangle is formed.

Method I: 
Case 1: All 3 points are selected from 3 non-collinear points..
# of ways = 1 way

Case 2: 2 points from non-collinear and 1 point from collinear ..
# of ways = 3C2 * 5C1 = 3*5 = 15 ways

Case 3 : 1 point from non-collinear and 2 points from collinear..
# of ways = 3C1 * 5C2 = 3*10 = 30 ways

Case 4 : All points from collinear.. But it'll not give us a triangle. So, we can rule out this case

Therefore, total # of ways = 1+15+30 = 46 ways

Method II : 
As already mentioned by others. 
Favorable cases = Total cases - Unfavorable cases

Total = 8C3 = 56
Unfavourable = Selecting all three points from set of collinear points = 5C3 = 10 

Therefore, Favorable cases = 56-10 = 46 ways