1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider a rectangle ABCD having 5,7,6,9 points in the interior of the line segments AB, CD , BC, 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 :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider a rectangle ABCD having $5,7,6,9$ points in the interior of the line segments $AB$, $CD , BC$, DA respectively. Let $\alpha$ be the number of triangles having these points from different sides as vertices and $\beta$ be the number of quadrilaterals having these points from different sides as vertices. Then $(\beta-\alpha)$ is equal to :

JEE MainJEE Main 2021Permutations and Combinations

Solution:

image
$\alpha=$ Number of triangles
$\alpha=5 \cdot 6 \cdot 7+5 \cdot 7 \cdot 9+5 \cdot 6 \cdot 9+6 \cdot 7 \cdot 9$
$=210+315+270+378$
$=1173$
$\beta=$ Number of Quadrilateral
$\beta=5 \cdot 6 \cdot 7 \cdot 9=1890$
$\beta-\alpha=1890-1173=717$