How many diagonals can an n-gon (a polygon with n sides ) have ?

Explanation

"A polygon of n-sides has n vertices".
`:.` "The number of st. lines joining the n-vertices is" `""^nC_2`.
`:.` "The number of diagonals is" `""^nC_2-n`
`= (n!)/(2!(n-4)!)-n=(n(n-1))/2-n`
`= (n^2-n-2n)/2=(n^2-3n)/2=(n(n-3))/2`