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 $=66-3+1=64$