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

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

(b) 63

(c) 64

(d) 65

Solution:

(c) 64

Number of straight lines joining 12 points if we take 2 points at a time $={ }^{12} C_{2}=\frac{12 !}{2 ! 10 !}=66$

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.

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

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