JEE Main202116 Mar 2021Evening ShiftMathematicsPermutation and CombinationActual
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
Options
- A795
- B1173
- C1890
- D717
Correct answer
D. 717
Step-by-step 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