Question

There are $12$ points lying on a circle. How many cyclic quadrilaterals can be formed with these points?

• A. $380$
• B. $500$
• C. $455$
• D. $495$

Answer 1

Answer: (D)

$495$

$12$ Points on a circle

Quadrilatral $\Rightarrow$Number of sides $=4$

Since the point lies on a circle

$\Rightarrow$No three points are collinear

$\Rightarrow$ selecting $4$ points of $12$

$\Rightarrow$ Number of quad ${=}^{12}{C}_4$

$=\frac{12!}{4!\times 7!}=\frac{12\times 11\times 10\times 9}{4\times 3\times 2}=495$