In 4*4 matrix what is probability of forming a triangle when any three points are chosen at random?

Ans. 516/560

• to form a triange, we need 3 points
  
  n(S)= 16c3 = 560
  
  from 3 collinear point, we can't form a triangle,
  no. of such combination = 4*4c3 + 4*4c3 + 2*4c3 + 4 = 44
  [these are for same rows,columns,diagonals & oppisite to diagonals]
  
  n(E)= triangle formation = 16c3 - 44 = 560-44 = 516
  
  probability of forming a triangle = p = n(E)/n(S) = 516/560.
  
  
  is it right????
• 10 years agoHelpfull: Yes(111) No(9)
• 512/560
  During the selection of three point selecting the tthree collinear piont then for each point we draw the three line the number of line is 16*3 = 48, 560-48= 512
• 10 years agoHelpfull: Yes(8) No(3)
• the opposite OF DIAgonals means the three collinear points on both sides of diagonals parallel to diagonal,and there are 2 diagonals means 2 more collinear points of line.
• 10 years agoHelpfull: Yes(7) No(2)
• P(S) = 16c3 = 560
  no.of. chances for selecting 3 points which are on the same line
  = 4*4c3 + 4*4c3 + 2*4c3 + 4*3c3 = 52
  (columns)+(rows)+(diagonals)+(beside diagonals 3 dots in diagonal shape)
  P(E) = 560 - 52 = 508
  
  Probability = 508/560
  
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• 10 years agoHelpfull: Yes(4) No(6)
• @rakesh : please explain the +4 in the end of your solution
• 10 years agoHelpfull: Yes(3) No(1)
• [Ramesh Babu]
  P(S) = 16c3 = 560
  no.of. chances for selecting 3 points which are on the same line
  = 4*4c3 + 4*4c3 + 2*4c3 + 4*3c3 = 44
  (columns)+(rows)+(diagonals)+(beside diagonals 3 dots in diagonal shape- something like / and )
  P(E) = 560 - 52 = 508
• 8 years agoHelpfull: Yes(1) No(0)
• @Rakesh opposite to diagonals means?
• 10 years agoHelpfull: Yes(0) No(3)
• common no.'s are those that will give remainder of 2 when divided by 5 or 7....they will be repeated each time.
• 10 years agoHelpfull: Yes(0) No(2)
• sorry to inform you guys that if the 4* 4 matrice is here then the no of points in one line will be 5 and there will be 5 lines so the no of total ponits are 25.
  And the ans will be:-9/46
  am i right friends?
  
• 9 years agoHelpfull: Yes(0) No(9)
• first of all make it sure there are 25 points as there are 5*5 lines required to make 4*4 matrix....
  total ways of selecting 3 points =5c3=2300
  now the no of combinations of getting 3 or more collinear points= 5*5c3 (rows) + 5*5c3(columns)+2*5c3(diagonals)+2*4c3(for 45degree line formed above and below principal diagonal)+2*4c3(for 45 degree lines formed below and above other diagonal) +2*2*3c3(for 45 degree line formed above and below two diagonals formed )= 140
  
  so ans=(2300-140)/2300=2160/2300=108/115
• 9 years agoHelpfull: Yes(0) No(2)