Consider a rectangle A B C D having 5 , 6 , 7 , 9 points in the interior of the line segments A B ,   B…

Consider a rectangle ABCD having 5,6,7,9 points in the interior of the line segments AB, BC, CD, DA respectively. Let α be the number of triangles having these points from different sides as vertices and β be the number of quadrilaterals having these points from different sides as vertices. Then β-α is equal to
  1. 795
  2. 1173
  3. 1890
  4. 717

Solution

α= Number of triangles

α=5·6·7+5·7·9+5·6·9+6·7·9

=210+315+270+378

=1173

β= Number of Quadrilateral

β=5·6·7·9=1890

β-α=1890-1173=717

Asked in: JEE Main 2021 (16 Mar Shift 2)

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