Consider a rectangle A B C D having 5 , 6 , 7 , 9 points in the interior of the line segments A B , B C , C D , D A respectively. Let α be the number of triangles having these points from different si

Question

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

TestHub · Accepted Answer

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

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