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Question

There are 12 points (A1,A2,...,A12) in a plane, where (A1,A2,A3,A4) are collinear to each other and (A5,A6,A7,A8) are collinear to each other. If no points other than these two set of points are collinear, then the total number of straight lines that can be formed using these 12 points is

A
54
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B
56
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C
60
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D
62
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Solution

The correct option is B 56Total number of straight lines that can be formed using these points without any restrictions is 12C2 But four points are collinear due to which number of lines that can be formed using this points, 4C2 should be subtracted but one line passing through all four points must be counted. And same thing will be followed for the other set of collinear points. So, the total number of straight lines is 12C2−4C2+1−4C2+1=56

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