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

Correct answer marked below

216

156

Correct

142

140

135

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Preview

Official Explanation

Official

A circle (unique) can always be drawn through 3 points (non-collinear).

Ideally, using the 11 points, we should have got

_{11}C_{3} = 165

circles.

But, the 5 points which are already in a single circle, would have been counted as

_{5}C_{3} = 10

circles.…

Comments

Be the first to share your thoughts and help others understand it better.

What this question tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.