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The sides AB, BC, CA of a triangle ABC h...

The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 triangles that can be constructed by using these points as vertices, is

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The correct Answer is:
205
Total number of points on sides of triangle is 12.
For triangle three points can be selected in `.^(12)C_(3)` ways.
But selection of three points from any of the sides will not form triangle.
So, number of triangles `= .^(12)C_(3)- .^(3)C_(3)- .^(4)C_(3)- .^(5)C_(3)`
`=220-15=205`
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