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
