There are 12 points in a plane, out of which 3 points are collinear.

Question:

There are 12 points in a plane, out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

Solution:

To get a straight line we just need to join two points. There are 12 numbers of

points. Therefore, there is ${ }^{12} \mathrm{C}_{2}=66$ number of straight lines. Among the 12 points, there are 3 points which are collinear. That means joining those 3 lines give a single straight line. That means the real number of straight lines present in the table is $=\left(66-{ }^{3} C_{2}+1\right)$ $=(66-3+1)=64$.

 

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