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  4. There are 16 points in a plane, out of which 6 points are collinear. Then, how many straight lines can be drawn using these lines.

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Q. There are 16 points in a plane, out of which 6 points are collinear. Then, how many straight lines can be drawn using these lines.

Rajasthan PETRajasthan PET 2001

Solution:

Required number of lines = (number of lines made by 16 points) - (number of lines made by 6 collinear points) + 1 $ {{=}^{16}}{{C}_{2}}{{-}^{6}}{{C}_{2}}+1 $
$ =\frac{16\times 15}{2\times 1}-\frac{6\times 5}{2\times 1}+1 $
$ =120-15+1 $ $ =106 $