Question

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

Answer 1

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.

$_{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!}$

⇒ $_{8}^{5}\textrm{C}= \frac{8!}{5!(8-5)!}$

⇒$_{8}^{5}\textrm{C}= \frac{8!}{5!\times 3!} \\\\_{8}^{5}\textrm{C} = \frac{8\times 7\times 6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times3\times2\times1} = \frac{336}{6}$

∴ $_{8}^{5}\textrm{C}= 56$

∴ With eight point lies on circle, we can make 56 pentagons using five points as vertices