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Question

Let there be 16 points in a plane out of which 6 lie on one line and 5 lie on other line, then the correct option(s) among the following is/are
  1. Total straight lines that can be formed using these points are 95
  2. Total triangles that can be formed using these points are 530
  3. Total circles that can be formed using these points are 256
  4. Total quadrilaterals that can be formed using these points are 1490


Solution

The correct options are
B Total triangles that can be formed using these points are 530
D Total quadrilaterals that can be formed using these points are 1490
Total straight lines that can be formed from 16 points = 16C2
Required number of ways
Since total points are 16, but 6 are collinear and other 5 are also collinear.
Required number of ways = 16C2 6C2 5C2+1+1=97
(two lines will be obtained from collinear points)

Total triangles that can be formed from 16 points = 16C3
Since total points are 16, but 6 are collinear and other 5 are also collinear.
Required number of ways = 16C3 6C3 5C3=530

Total circles that can be formed from 16 points = 16C3
Since total points are 16, but 6 are collinear and other 5 are also collinear.
Required number of ways = 16C3 6C3 5C3=530

Total quadrilaterals that can be formed from 16 points = 16C4
Since total points are 16, but 6 are collinear and other 5 are also collinear.
Also, for making quadrilaterals three collinear points can't be taken,
Required number of ways = 16C4 6C4 5C4 6C3× 10C1 5C3× 11C1=1490

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