Consider a rectangle $ABCD$ having $5,6,7,9$ points in the interior of the line segments $AB, BC, CD, DA$ 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 $\left(\beta -\alpha \right)$ is equal to

• A

  $795$
• B

  $1173$
• C

  $1890$
• Correct answer
  D

  $717$

Hence, the correct answer is option: 'D'.