There is a set of 36 distinct points on a plane with the following characteristics:
* There is a subset A consisting of fourteen collinear points.
* Any subset of three or more collinear points from the 36 are a subset of A.
How many distinct triangles with positive area can be formed with each of its vertices being one of the 36 points? (Two triangles are said to be distinct if at least one of the vertices is different)
a. 7140
b. 4774
c. 1540
d. 6776

• The given data indicates that 14 points are collinear and remaining 22 points are non collinear.
  A triangle can be formed by taking 1 points from 14 and 2 points from 22 (or) 2 points from 14 and 1 points from 22 (or) 3 points from 22
  ⇒ 14C1×22C2+14C2×22C1+22C3= 6776
• 9 years agoHelpfull: Yes(31) No(1)
• 6776
  36c3-14c3
  
• 9 years agoHelpfull: Yes(11) No(1)
• RRB Chennai Problem:
  Q:-How to solve question in how many in 8 questions can be selected in a question paper containing 12 questions so that it always contains question number 1,5 and 10  ?
  Solution:- since total n. of questions=12
  3 question mandatory for selection
  Therefore remaining n question (n)=12-3=9
  Since 8 question out 3 question mandatory selection (r)=8-3=5
  Therefore total n of ways of selection of questions be= nCr=9C5=!9/(!5 × !4) =126(Ans:)
  Er. Sudhir Kumar!!😍🚉
• 9 years agoHelpfull: Yes(2) No(6)
• 36c3 - 14c3 = 6776
• 9 years agoHelpfull: Yes(2) No(1)
• 36c3-14c3======6776
• 9 years agoHelpfull: Yes(1) No(3)
• as here given no of collinear point=14
  so, no of non- collinear poin=36-14=22
  triangle can be formed by taking 1 point from collinear(14) and 2 point from non collinear (22) or 2 point from collinear(14) and 1 points from non collinear(22) or taking 3 points from non collinear(22)
  i:e, 14C1*22C2+14C2*22C1+22C3= 6776
• 9 years agoHelpfull: Yes(1) No(0)
• what if we take 3 points from 14 also?
  
  then answer will be =14c1*22c2+14c2*22c1+22c3+14c3=7140
  
• 9 years agoHelpfull: Yes(0) No(17)
• 36 C3-14C3=6776
• 9 years agoHelpfull: Yes(0) No(4)
• 36C3 - 14C3= 6776
• 9 years agoHelpfull: Yes(0) No(0)
• d is the answer
• 9 years agoHelpfull: Yes(0) No(0)
• 36c3-14c3=6776
• 9 years agoHelpfull: Yes(0) No(1)
• 36 C3-14C3=6776
• 7 years agoHelpfull: Yes(0) No(2)
• THERE ARE 22 POINTS COLLINEAR AND 14 POINTS NON-COLLINEAR.SO USING 3 POINTS ONE CAN FORM THE TRIANGLE.THEREFORE THE ANSWER IS
  (22C2*14C1)+(22C1*14C1)+22C3
  (OR)
  36C3-14C3
  ANSWER:6776
• 6 years agoHelpfull: Yes(0) No(0)
• 14C1*22C2+14C2*22C1+22C3=6776
• 5 years agoHelpfull: Yes(0) No(0)
• there are 36 points
  in that 14 points are collinear..means lies on the same line
  other than that 14 ,remaining are non collinear.
  non collinear point=>36-14=22
  for forming a triangle ,we need 3 points
  we can use two points on a collinear and one on non collinear poins=14c2*22+22c2*14+22c3
  22c3=may be the triangle can be formed only by non collinear points
  14*22c2+22*14c2+22c3
  by solving we will get 6776
• 5 years agoHelpfull: Yes(0) No(0)