Question

Here is 15 dots. if you select 3 dots randomly, what is the probability that 3 dots make a triangle?
a. 440/455

Answer 1

The picture of 15 dots is missing.

See the enclosed pictures.

Answer is = (15C3 - 3 × 5C3 - 5 - 2 × 3 - 2) / 15C3
= 412/455

15C3 = ways of selecting 3 vertices.
5C3 = number of ways of selecting 3 points from one row.
5 = number of columns
3 + 3 + 2 are inclined diagonals.