Mark the correct alternative in the following: 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

Question

Philoid · Accepted Answer

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

Mark the correct alternative in the following: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

Mark the correct alternative in the following:
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