Question

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 :

(1) 795

(2) 1173

(3) 1890

(4) 717

Answer 1

Correct answer is (4)

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