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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
Options
62
63
64
65
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Solution
64
Number of straight lines joining 12 points if we take 2 points at a time = 12C2
\[= \frac{12!}{2! 10!} = 66\]
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, give only one line.
∴ Required number of straight lines =\[66 - 3 + 1 = 64\]
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