There are 25 points in a plane Six of these are collinear and no other combination of 3 points are collinear How many different straight lines can be formed by joining these points?

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Solution

A straight line is formed by joining any two points
∴ The number of straight lines that can be formed by joining $25$ points is $^{25} C_{2}$
But $6$ points are collinear
∴ These $6$ points form only one line instead of $^{6} C_{2}$ lines
∴ The total number of lines that can be formed is $^{25} C_{2} -^{6} C_{2} + 1 = 286$

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