Question

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

Answer 1

56 pentagon.

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} = (n!)/(r!(n-r)!)`

⇒
`_(8)^(5)\textrm{C}= (8!)/(5!(8-5)!)`

⇒
`_(8)^(5)\textrm{C}= (8!)/(5!* 3!) \\\\_(8)^(5)\textrm{C} = (8* 7* 6*5*4*3*2*1)/(5*4*3*2*1*3*2*1) = (336)/(6)`

∴
`_(8)^(5)\textrm{C}= 56`

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