# 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 Points is - Mathematics

MCQ

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 points is

#### Options

•  216

• 156

•  172

• none of these

#### Solution

156
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 one circle.

$\therefore$  Required number of circles = 165 - 10 + 1 = 156
Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 19 | Page 26