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

• ans is 413/455
  
  15+14+13=42
  455-42=413
  413-1(co-liner condition elimination) =412
  
  ans:412/455
• 8 years agoHelpfull: Yes(5) No(0)
• in think ans will be 414/455.
  455-(3*5c3+5+6)=414.
  but am not sure
• 8 years agoHelpfull: Yes(4) No(4)
• 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(4) No(2)
• 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 probability could be 412/455.
• 5 years agoHelpfull: Yes(2) No(0)
• take a look on => http://www.examveda.com/here-is-15-dots-if-you-select-3-dots-randomly-what-is-the-probability-that-3-dots-make-a-triangle-1458/
  
  also =>
  http://www.arraypeers.com/view_post/1324/Here+is+15+dots.+If+you+select+3+dots+randomly,+what+is+the+probability+that+3+dots+make+a+triangle%3F
• 7 years agoHelpfull: Yes(1) No(1)
• ans is c. (449/455)
  15c3 = 455
  1+2+3=6
  455-6=449
  449/455
  I am not sure.
• 8 years agoHelpfull: Yes(0) No(3)
• as we can choose 3 dots in 15c3 manner.
  the no. of chances to have triangles are 15c3....as no. of chances that these 3 dots sholud be collinear is 6.
  455-6=449
  we can have 5 lines of 3 dots .. so choosing 3 dots from each line can be 5 and all the points lie in one line be 1.so total will be 6;
  
  so prob is 449/455
• 8 years agoHelpfull: Yes(0) No(2)
• Selecting 3 dots out of 15 is 15C3 = 455.
  
  And 3 dots are collinear so the triangle will not be formed.
  Now 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 probability could be 412/455.
• 1 year agoHelpfull: Yes(0) No(0)