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प्रश्न
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
उत्तर
Number of triangles formed joining the 18 points, taking 3 points at a time =\[{}^{18} C_3 = \frac{18}{3} \times \frac{17}{2} \times \frac{16}{1} = 816\]
Number of straight lines formed joining the 5 points, taking 3 points at a time =\[{}^5 C_3 = \frac{5}{3} \times \frac{4}{2} \times \frac{3}{1} = 10\]
∴ Required number of triangles =\[816 - 10 = 806\]
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