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Question

In a plane there are $$10$$ points out of which $$4$$ are collinear. How many triangles can be formed with these points as vertices.


A
116
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B
155
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C
160
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D
185
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Solution

The correct option is A $$116$$
There are $$3$$ ways for calculating the number of triangles
1. Choose any $$3$$ from $$6$$ non-collinear points
2. Choose any $$1$$ from $$4$$ collinear points and any $$2$$ from $$6$$ non collinear points.
3. Choose any $$2$$ from $$4$$ collinear points and $$1$$ from $$6$$ non - collinear points
Number of Triangles $$=^4C_1 \times^6C_2 +^6C_3+^4C_2 \times ^6C_1=116$$

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