4*4 matrix find probability of creating a triangle with the help of 3 points

• 129/140
  Explanation:
  
  total outcome=16c3
  unfavorable outcome:
  if we select
  all three point from a row = 4c3*4!/3!=16;
  all three point from a col = 4c3*4!/3!=16;
  all thee point from on diognal=2*(3c3+4c3+3c3)=12;
  so total unfavorable outcome=44;
  so the required probabilty=1-44/560=129/140;
  
  
• 11 years agoHelpfull: Yes(14) No(5)
• 13/14
  Explanation:
  p(create a triangle)= 1 - p(triangle never formed)
  =1 - (10*4C3)/16C3 [10= 4 rows 4 cols and 2 diagonals]
  
• 11 years agoHelpfull: Yes(8) No(5)
• 129/140
  Explanation:
  Probability unfavorable outcomes=10*4C3/16C3+4*3C3/16C3
  [4 rows 4cols 2 diagonals having 4 points in same line(i.e 4+4+2=10) and 4 diagonals having only 3 points in same line]
  (10*4+4)/16C3=4*11*3*2/(16*15*14)=11/140
  So Probability of favorable outcomes=1-11/140=129/140
• 11 years agoHelpfull: Yes(7) No(1)
• ans is 129/140
  collinear 4 points=10 (4 row 4col 2 diag)
  collinear only 3 points=4 (diagonolly)
  so no. of tritangle form= 16c3-10x4c3-4x3c1=516
  prob=516/560= 129/140
• 11 years agoHelpfull: Yes(3) No(0)
• the only way there will be no triangles formed when u select all 3 points in the same line forming a straight line that is by 4c3 in each row or column so total ways by which these st lines be formed is by 4c3*8=32
  so 16c3-32=528
  so probability of forming triangle is 528/560
• 11 years agoHelpfull: Yes(2) No(3)
• yup u r right... total ways of forming a line using three points is
  4* 4C3 (rows) //(4 rows if selecting 3 point from each row)
  + 4*4C3 (columns) //(4 rows if selecting 3 point from each column )
  + 2*4C3 (diagonals) //(2 diagonals having 4 point selecting 3 from it)
  + 4 (shorter diagonals) //(matrix begin with (1,1) then first diagonal (1.2)(2,3)(3,4)
  second (1,3)(2,2) (3,1) third (2,1)(3,2)(4,3) fourth (2,4)(3,3)(4,2)
  = 44
  Thus 1 - (44/560) will be the ans 129/140
• 10 years agoHelpfull: Yes(2) No(0)
• Probality???? Is there any unsure event there???
• 11 years agoHelpfull: Yes(1) No(0)
• =1-24/560
  =536/560
  =67/70
  
• 11 years agoHelpfull: Yes(1) No(2)
• @ anubhav u forget that at above the diagonal and below the diagonal their are 3 points in diagonally make a fig. and notice that
  1 2 3 4
  5 6 7 8
  9 10 11 12
  13 14 15 16
  
  3 6 9 are also 3 points that make no triangle
  
• 11 years agoHelpfull: Yes(1) No(1)
• please mention the question correctly ....
• 11 years agoHelpfull: Yes(0) No(0)
• there is points 4x4 (i.e 16 points) find the total number of triangle form using 3 points of this 4x4 points.
• 11 years agoHelpfull: Yes(0) No(0)
• 16!/13!*3!
• 11 years agoHelpfull: Yes(0) No(4)
• please explain this question clearly...
  
• 11 years agoHelpfull: Yes(0) No(0)
• its probability>> 4*4 matrix where there is 16 points 3 points can be selected thats is 16c3=560 ways ok now tell me the probability among this how many will form a triangle (means selecting 3 points out of 16 whts is probability)..............will be telling ur ans shortly
• 11 years agoHelpfull: Yes(0) No(0)
• guys any1 can give me an ideal soln of this sum...if yes...pls give !!!
• 11 years agoHelpfull: Yes(0) No(0)
• thanks krishanu !!!
• 11 years agoHelpfull: Yes(0) No(0)
• so the ultimate ans is 33/35
• 11 years agoHelpfull: Yes(0) No(4)
• please anyone explain the right answer.
  
• 11 years agoHelpfull: Yes(0) No(0)
• 132/560 = 33/140
• 11 years agoHelpfull: Yes(0) No(0)
• sambit can u plz explain how you solved it.
• 11 years agoHelpfull: Yes(0) No(0)
• 1- (10*4c3 - 4)/16c3
• 11 years agoHelpfull: Yes(0) No(0)
• the ans of @roshan jha and @prem kumar is right. i.e. 129/140 . rest all are wrong.
  plz correct them.
  :)
• 11 years agoHelpfull: Yes(0) No(0)