Question

ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked on the sides AB, BC, CD, and DA, respectively. The number of triangles with vertices on different sides is a. `270` b. `220` c. `282` d. `342`
A. 220
B. 270
C. 282
D. 342

Answer 1

Correct Answer - D
Total number of triangles=Number of triangles with vertices on sides
`[(AB,BC,CD)+(AB,BC,DA)+(AB,CD,DA)+(BC,CD,DA)]`
`=.^(3)C_(1)xx.^(4)C_(1)xx.^(5)C_(1)+.^(3)C_(1)xx.^(4)C_(1)xx.^(6)C_(1)+.^(3)C_(1)xx.^(5)C_(1)xx.^(6)C_(1)+.^(4)C_(1)xx.^(5)C_(1)xx.^(6)C_(1)`
`=60+72+90+120=342`