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  4. In a plane there are 3 straight lines concurrent at a point 'P', 4 others which are concurrent at a point Q and 5 others which are concurrent at a third point R . Supposing no other three intersect at any point and no two are parallel then the number of triangles that can be formed by the intersection of these straight lines is :

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Q. In a plane there are 3 straight lines concurrent at a point 'P', 4 others which are concurrent at a point Q and 5 others which are concurrent at a third point R . Supposing no other three intersect at any point and no two are parallel then the number of triangles that can be formed by the intersection of these straight lines is :

Permutations and Combinations

Solution:

${ }^{12} C _3-\left({ }^3 C _3+{ }^4 C _3+{ }^5 C _3\right)=205$