Question

Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given point is :

A. 216 

B. 156 

C. 172 

D. none of these

Answer 1

Option : (B)

We need at least three points to draw a circle that passes through them. 

Now, 

Number of circles formed out of 11 points by taking three points at a time = ¹¹C₃ 

= 165 

Number of circles formed out of 5 points by taking three points at a time = ⁵C₃ 

= 10 

It is given that 5 points lie on once circle. 

∴ Required number of circles = 165 – 10 + 1 

= 156