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Question

There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is


A

62

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B

63

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C

64

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D

65

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Solution

The correct option is C

64


Number of straight lines joining 12 points if we take 2 points at a time = 12C2

=12!2!10!=66

Number of straight lines joining 3 points if we take 2 points at a time = 3C2=3 But, 3 collinear points, when joined in pairs, given only one line.

Required number of straight lines = 66 - 3 + 1 = 64


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