Question

Calculate the maximum number of diagonals that can be drawn in an octagon using the suitable formula

Answer 1

$n=8$
Number of diagonals $={}^n{C}_2-n$
$={}^8{C}_2-8$
$=\frac{1}{2}{}^8{P}_2-8$ $=\frac{8\times 7}{2}-8$
$=28-8$
Number of diagonals $=20$

OR

$n=8$
Number of diagonals $={}^n{C}_2-n$
$=\frac{n(n-3)}{2}$
$=\frac{8(8-3)}{2}$ $=\frac{8\times 5}{2}$
Number of diagonals $=20$.