There are 10 points in three parallel planes, first plane contain 5 points, second plane contain 3 points and third plan contain rest of them, then how many traingles to be formed ?

1)104
2)109
3)105
4)106
5)None of these

• For forming a triangle we need 3 points therefore from 10 points we can form 10c3 triangles but
  out of 10 points 5(1st line),3(2nd line),2(3rd line) points are collinear so we have to eliminate those points so that sub those colinear points from 10c3
  ie, =(10c3)-(5c3)-(3c3)
  =120-10-1
  =109
• 5 years agoHelpfull: Yes(18) No(2)
• For forming a triangle,
  1. You need 3 points
  2. Those points should not be in the same plane.
  
  Let us name the planes as p2, p3, p5 where the the number denotes the number of points it has
  Therefore if you calculate every possible case:
  consider taking 2 points from 1st plane and then 1 point from 2nd plane that is
  1. Take 2 points from p2 and one from p3 i.e = 2c2 x 3c1 = 3
  2. Take 2 points from p2 and one from p5 i.e = 2c2 x 5c1 = 5
  3. Take 2 points from p3 and one from p5 i.e = 3c2 x 5c1 = 15
  4. Take 2 points from p3 and one from p2 i.e = 3c2 x 2c1 = 6
  5. Take 2 points from p5 and one from p2 i.e = 5c2 x 2c1 = 20
  6. Take 2 points from p5 and one from p3 i.e = 5c2 x 3c1 = 30
  
  Now one more case remain in which you can choose 1 point from each plane = 5c1 x 3c1 x 2c1 = 30
  
  Adding all up (30 + 30 +20 + 15 + 5 + 6 + 3) we get 109 [Answer]
• 5 years agoHelpfull: Yes(6) No(0)
• Lets consider:
  Plane 1: 2 points
  Plane 2 : 3 points
  Plane 3: 5 points
  
  No. of triangle b/w Plane 1 & 2: 4C3 + 4C3
  No. of triangles b/w Plane 1 &3: 6C3 + 6C3
  No. of triangles b/w Plane 2&3 : 6C3 + 6C3 +6C3
  
  Summation of all these we get: 108
• 5 years agoHelpfull: Yes(3) No(16)
• 109
  Line 1 - 5 points can make 4 combination of each 5*4 = 20(each point in plane 2 with plane 1) so 20*3 - 60
  Same follow for plane 1to 3 so 20*2 - 40.
  For plane 2 to 3 - 9
  SO 60+40+9=109
  We can say--5^3 - 75
  5^2-25
  3^2 - 9
  75+25+9 = 109
• 5 years agoHelpfull: Yes(3) No(1)
• 3 point needs to form triangle.
  
  5 point are collinear,in one plane and 3 point are collinear in other plane.these point will not form triangle.
  so 10c3-5c3-3c3=109 triangles
• 5 years agoHelpfull: Yes(2) No(0)
• The Tips & Tricks to solve this problem is Here https://youtu.be/NwOOffNdNjM
• 5 years agoHelpfull: Yes(0) No(6)
• 109 10c3-5c3-3c3 =109
• 5 years agoHelpfull: Yes(0) No(0)
• 10c3-5c3-3c3=109
• 5 years agoHelpfull: Yes(0) No(0)
• The answer is 109
• 3 years agoHelpfull: Yes(0) No(0)