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

Answer 1

The correct option is 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 $={}^3{C}_2=3$ But, 3 collinear points, when joined in pairs, given only one line.

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