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

Options

A. 220
B. 270
C. 282
D. 342

Answer

D

Explanation

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`