Question

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

• A. $45$
• B. $40$
• C. $39$
• D. $38$

Answer 1

The correct option is B $40$

If all the 10 points are non-collinear, then the number of possible lines is $(\frac{10}{2})$

If 4 points are non-collinear then the number of possible lines is $(\frac{4}{2})$and If 4 points are collinear, then the number of possible lines through these points equals 1.So, we need to subtract $((\frac{4}{2})-1)$ from the total points $(\frac{10}{2})$

So, the total number of straight lines is $(\frac{10}{2})-(\frac{4}{2})+1$=40

Hence, Option B is correct.