Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?

Solution(By Examveda Team)

Total ways of selecting 3 dots out of 15 is 15C3 = 455.
If 3 dots are collinear then triangle may not be formed.
Now look at the above diagram. If we select any 3 dots from the red lines they may not form a triangle.
They are 3 x 5C3 = 30. If we select the three letters from blue lines, they may not form a triangle.
They are in total 5 ways. Also there are 6 others lines which don't form a triangle.
Also another two orange lines. Total = 30 + 5 + 6 + 2 = 43.
So we can form a triangle in 455 - 43 = 412.
So probability could be 412/455.