How many pentagons can you make using five points as vertices?

Answer:56 pentagon.Step-by-step explanation:Here is the complete question: Eight point lies on the circle. How many pentagons can you make using five points as vertices?Given: Five points on vertices.Using the combination formula to find the number of pentagon.[tex]_{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!}[/tex]⇒ [tex]_{8}^{5}\textrm{C}= \frac{8!}{5!(8-5)!}[/tex]⇒[tex]_{8}^{5}\textrm{C}= \frac{8!}{5!\times 3!} \\\\_{8}^{5}\textrm{C} = \frac{8\times 7\times 6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times3\times2\times1} = \frac{336}{6}[/tex]∴ [tex]_{8}^{5}\textrm{C}= 56[/tex]∴ With eight point lies on circle, we can make 56 pentagons using five points as vertices