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There are ten points in the plane, no th...

There are ten points in the plane, no three of which are coolinear. How many different lines can be drawn through these points ?

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There are ten points `P_(1), P_(2),.., P_(10)`.
For one line two points are required.
Through point `P_(1)` there will be 9 lines when `P_(1)` is joined with any of the nine other points.
Similarly, there will be nine lines passing through each point.
So, number of lines is `9xx10` or 90.
But there is double counting in above answer. Why ?
One of the nine lines passing through point `P_(1) " is" P_(1) P_(2). "But" P_(1) P_(2)` is also one of the lines passing through point `P_(2)`.
Thus, line `P_(1)P_(2)` and similarly each line is counted twice. Therefore, actual number of lines is `(90)/(2)=45`.
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