Question

Six points lie on a circle. How many quadrilaterals can be drawn joining these points?

• A. 72
• B. 36
• C. 25
• D. 15
• E. 120

Hint:

Any 4 vertices of a circle form a convex quadrilateral. Use \(\binom{n}{4}\).

Answer 1

The Correct Option is D

Step 1: Condition.
To form a quadrilateral, we choose 4 vertices from 6 points on the circle.

Step 2: Apply combination.
\[ \binom{6}{4} = \frac{6 \times 5}{2 \times 1} = 15 \]
Final Answer:
\[ \boxed{15} \]