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in Mathematics by (71.2k points)

ABCD is a convex quadrilateral. 3, 4, 5 and 6 points are marked on the sides AB, BC, CD and DA resp. The number of triangles with vertices on different sides are_____ 

(a) 270 

(b) 220 

(c) 282 

(d) 342

1 Answer

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Best answer

Correct option: (d) 342

Explanation:

Number of triangles with vertices on AB, BC, CD = 3C1 × 4C1 × 5C1 

with vertices on sides AB, BC, DA = 3C1 × 4C1 × 6C1 

with vertices on sides AB, CD, DA = 3C1 × 5C1 × 6C1 

with vertices on sides BC, CD, DA = 4C1 × 4C1 × 6C1 

Total triangles = (3C1 × 4C1 × 5C1) + (3C1 × 4C1 × 6C1) + (3C1 × 5C1 × 6C1+ (4C1 × 5C1 × 6C1)

= (3 × 4 × 5) + (3 × 4 × 6) + (3 × 5 × 6) + (4 × 5 × 6)

= 342

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