JEE PYQ: Permutation And Combination Question 1
Question 1 - 2021 (16 Mar Shift 2)
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:
(1) 795
(2) 1173
(3) 1890
(4) 717
Show Answer
Answer: (4)
Solution
$\alpha = 5 \cdot 6 \cdot 7 + 5 \cdot 7 \cdot 9 + 5 \cdot 6 \cdot 9 + 6 \cdot 7 \cdot 9 = 210 + 315 + 270 + 378 = 1173$. $\beta = 5 \cdot 6 \cdot 7 \cdot 9 = 1890$. $\beta - \alpha = 1890 - 1173 = 717$.
BETA
