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. 438/455

• 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(12) No(4)
• Was there any figure given?
• 9 years agoHelpfull: Yes(6) No(0)
• PICTURE IMAGE LINK 1ST SEARCH THIS LINK THEN SEE SOLUTION
  
  http://2.bp.blogspot.com/-CBrHd-VHdxU/VdIk1gDF4UI/AAAAAAAAMzg/3XKqj0-mIZI/s1600/lines.png
  
  
  total possibilities=4c3=455
  
  now we have to find the number of dots that do not make a triangle;
  
  3 dots from each row are collinear.So they will not form a triangle.thus total dots from each row possible=3*5c3=30
  
  Each column is collinear.So 5 straight lines formed.
  
  now consider the dots [ { (1,1),(2,2),(3,3)} , {(1,2),(2,3),(3,4)} ,{ (1,3),(2,4).(3,5)} ] each set here does not make a triangle as they are collinear.Same goes for other three points {(1,3),(2,2),(3,1)} {(1,4),(2,3),(3,2)},{(1,5),(2,4),(3,3)}.So 3+3=6 straight lines that does not make a triangle.Also each dots from diagonals are collinear and thus does not make a triangle.So again 2 straight lines formed.
  
  So total dots that does not make a triangle are=30+5+6+2=43
  
  So no of triangles formed are=455-43=412
  
  probability=412/455
  
• 9 years agoHelpfull: Yes(6) No(1)
• 412/455 is correct ans.This question asked in TCS
• 9 years agoHelpfull: Yes(3) No(0)
• total ways to select 3 points = 15C3 = 455
  
  when it will not form a triangle = 15C3 - when it will form a line.
  
  horizontal lines
  => from first line OR from second line OR from third line
  => 5C3 OR 5C3 OR 5C3
  => 10 + 10 + 10 = 30
  
  Similarly , vertical lines
  => From first vertical line OR second vertical line ------ OR fifth vertical line
  => 3C3 + 3C3 + 3C3 + 3C3 + 3C3
  => 5
  
  diagonal lines
  from left towards right = 3
  from right towards left = 3
  so total 6
  
  when it will not form a triangle = 455 - (30 + 5 + 6) = 414
  
  probability = 414/455
• 8 years agoHelpfull: Yes(3) No(0)
• Ans is 440/455
• 9 years agoHelpfull: Yes(1) No(7)
• None of them.
  Correct Anser is 412/455.
  
• 9 years agoHelpfull: Yes(1) No(1)
• kaisa bhai
  
• 9 years agoHelpfull: Yes(0) No(1)
• Jugal Khajuriya can u explain plzz
• 9 years agoHelpfull: Yes(0) No(2)
• please explain this question how to solve it??
• 9 years agoHelpfull: Yes(0) No(1)
• 412/455 IS THE RIGHT ANSWER
• 9 years agoHelpfull: Yes(0) No(3)
• sorry I read the wrong questions
• 9 years agoHelpfull: Yes(0) No(1)
• mithilesh bhai copy q krta campus gate sa wo ghat solution hai kuch line clnear bana usko dhek
• 9 years agoHelpfull: Yes(0) No(3)
• a.440/455ans
• 9 years agoHelpfull: Yes(0) No(3)
• Please can any one explain me the correct answer ??
• 9 years agoHelpfull: Yes(0) No(2)
• Figure for ques is =>
  
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  Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?
• 8 years agoHelpfull: Yes(0) No(0)