There are 10 points in a plane and 4 of them are collinear.

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

Solution:

(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, give only one line.

 

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

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now