Three sides of a triangle PQ, QR, and RP contains 5, 6 and 3 points respectively. What is the max number of triangles can be made using these points.

• answer is 333.
  here there are 5+6+3 =14 points from which triangle can be made. there for number of triangles made out of it is 14C3.
  but as triangle cannot be made out of collinear points therefore total number of triangle would be
  14C3-3C3-6C3-5C3
  =333.
• 11 years agoHelpfull: Yes(80) No(0)
• given triangle sides have 5,6,3 points
  now total we have 14 points.in that to form a triangle we need 3 points
  so we have total of 14c3 triangles.but there are also 5,6,3 collinear points from which we cant form a triangle.
  
  so the total triangles are 14c3-(5c3+6c3+3c3)=333
• 11 years agoHelpfull: Yes(11) No(0)
• (14!/(3!*11!))-(5!/(2!*3!)+6!/(3!*3!)+3c3)=333.
  ans is 333.
• 11 years agoHelpfull: Yes(3) No(1)
• all points on same line are colinear so they cannot contribute in formation of a triangle. no of triangles that can be formed will be 6*5*3
• 11 years agoHelpfull: Yes(2) No(10)
• yes i think Sweta is correct.
• 11 years agoHelpfull: Yes(1) No(0)
• 12c3/ 5!*6!*3!
  12 total pts with 5, 6 and 3 pts gettin collinear
• 11 years agoHelpfull: Yes(1) No(0)
• =(14!/3!*11!)-4-5-2
• 11 years agoHelpfull: Yes(0) No(5)
• ans is 6*5*3=90
• 11 years agoHelpfull: Yes(0) No(4)
• Doubt !! @Sweta yadav
  If we take pq,qr,rp as lines then joining 2 points of any 2 sides forms triangle.
  then 63(6*5+3*6+3*5) extra triangles.
  Then ans is 333+63 =396
  
• 11 years agoHelpfull: Yes(0) No(3)
• s manoj is crct
  
• 11 years agoHelpfull: Yes(0) No(1)
• Total 333 triangles will be made !!!
• 11 years agoHelpfull: Yes(0) No(0)