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There are 10 points on a plane of which ...

There are 10 points on a plane of which 5 points are collinear. Also, no three of the remaining 5 points are collinear. Then find (i) the number of straight lines joining these points: (ii) the number of triangles, formed by joining these points.

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(i) Line is formed by joining two points. Hence, the number of lines is `.^(10)C_(2)`. But joining any points from 5 collinear points gives the same line. Again, 2 points are selected from 5 in `.^(5)C_(2)` ways or lines joining collinear points is taken `.^(5)C_(2)(=10)` times. Then the number of straight lines `= .^(10)C_(2)-10+1=36`
(ii) For a triangle, three non-collinear points are required. Three points from 5 collinear points does not form triangle. Hence, number of triangles is `.^(10)C_(3)- .^(5)C_(3)`.
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