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Question
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
Solution
Number of straight lines formed joining the 18 points, taking 2 points at a time = \[{}^{18} C_2 = \frac{18}{2} \times \frac{17}{1} = 153\]
But, when 5 collinear points are joined pair wise, they give only one line.
∴ Required number of straight lines =\[153 - 10 + 1 = 144\]
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