Question 24

There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is

Solution
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Since we need distinct straight lines, we can form a line by choosing one point from collinear points and one from non-collinear points, or it can be formed by selecting two points from non collinear points, or there will be one unique line which can be formed by joining any two points from the five collinear points. 

=> Total number of straight lines = $$^5C_1\times\ ^5C_1+\ ^5C_2+1=25+10+1=36$$

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