Question

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is

• A. 45
• B. 40
• C. 39
• D. 38

Answer 1

The correct option is B

40

Number of straight lines formed by joining the 10 points if we take 2 points at a time

${}^{10}{C}_2=\frac{10}{2}\times \frac{9}{1}=45$

Number of straight lines formed by joining the 4 points if we take 2 points at a time

${}^4{C}_2=\frac{4}{2}\times \frac{3}{1}=6$

But, 4 collinear points, when joined in pairs, given only one line.

$\therefore$ Required number of straight lines = 45 - 6 + 1 = 40