Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?  Choose the most appropriate option
A) 440 / 455 B) 412 / 455 C) 434 / 455 D) 449 / 455 E) 438 / 455

Rationale: total ways of selecting 3 dots out of 15 is 15 c 3 = 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 5 c 3 = 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 do n ' 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 answer could be 412 / 455 . answer : b
Answer: B