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) 412/4228  B) 412/455  C) 412/429  D) 412/418  E) 412/419
I think there seem some problem with this question. Total ways of selecting 3 dots out of 15 is 15C315C3 = 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 5C35C3 = 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= 
<gadget id="calculator">30 + 5 + 6 + 2</gadget>
<output>43</output>
43. So we can form a triangle in 455 - 43= 
<gadget id="calculator">455 - 43</gadget>
<output>412</output>
412. So answer could be 412/455.   \Answer:412/455
<result>B</result>
Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?