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

a. 440/455
b. 434/455
c. 449/455
d. 436/455

• total ways to select 3 points = 15C3
  when it will not form a triangle = 15C3 - when it will form a line.
  horizontal lines = 3*5C3
  vertical lines = 5*3C3
  diagonal lines = 6
  probability = 414/455
  It may possible that i have made some mistake in calculation.
  Please correct me if so.
  But I think this is an easy way to calculate it.
• 9 years agoHelpfull: Yes(27) No(12)
• 
  
  total ways to select 3 points = 15C3
  when it will not form a triangle = 15C3 - when it will form a line.
  
  horizontal lines =(_) 3*5C3
  ._._._._._
  ._._._._._
  ._._._._._
  
  
  vertical lines = 5*3C3
  .-.-.-.-.
  |||||
  .-.-.-.-.
  |||||
  .-.-.-.-.
  |||||
  
  diagonal lines = 8
  .....
  /
  .....
  /
  .....
  
  
  ._._._._.
  
  ._._._._.
  
  ._._._._.
  
  
  
  ._._._._.
  / / /
  ._._._._.
  / / /
  ._._._._.
  
  
  probability = 412/455
  
• 9 years agoHelpfull: Yes(21) No(8)
• I think there seem some problem with this question. 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 answer could be 412/455.
  
• 9 years agoHelpfull: Yes(11) No(15)
• It shud be 438/455
• 9 years agoHelpfull: Yes(8) No(14)
• Check answer from here:- http://linkshrink.net/7lr4nE
  From above link you can conclude why the answer could be 412.
  Happy reading :)
• 9 years agoHelpfull: Yes(4) No(6)
• correct ans is 414/455
• 9 years agoHelpfull: Yes(2) No(5)
• 1 > 440/455
• 9 years agoHelpfull: Yes(1) No(10)
• total selection of 3 points to form triangle out of 15 points=15C3=455
  now we have to substract the collinear points which can form a line.
  horizontal lines of selection=5C3=10 and dis can be done in 3 ways so total horizontal lines=3*10=30.
  now vertical lines=5*3C3=5.
  total diagonals which can form a line=6.
  so total number of line=30+5+6=41
  total triangles=455-41=414
  hence probability=414455
• 9 years agoHelpfull: Yes(1) No(6)
• Please see link,http://linkshrink.net/7lr4nE
  the m4maths, reduce spaces, which make answer not understandable.
• 9 years agoHelpfull: Yes(1) No(3)
• give detail explaination
• 9 years agoHelpfull: Yes(0) No(4)
• i guess option d
  
• 9 years agoHelpfull: Yes(0) No(6)
• i dont know the question exactly .what is the answer that is related to base 10 asked in tcs 2015.
  ans options is a. 364 or b.436
• 9 years agoHelpfull: Yes(0) No(3)
• Ans is b
  No of horizontal triangle+no of vertical triangle-common triangle
  300+140-4=436/455
• 9 years agoHelpfull: Yes(0) No(3)
• please give the correct answer...
• 9 years agoHelpfull: Yes(0) No(0)
• Though the answer is 414/455. But the real question here is, how the **** am I going to select an option that is not available. Well done TCS. Kudos.....
• 7 years agoHelpfull: Yes(0) No(1)