Permutation and combination

Question

A diagonal of a polygon is defined to be a line joining any two non-adjacent vertices.
1.Show that the number of diagonals in a 5 sided polygon is(5 2) -5.

2.how many diagonals are their in 6 sided polygon?

3.Show that the number of diagonals in an n-sided polygon is n(n-2)/2.

Answer 1

#3 has a typo.
at each vertex, you can draw n-3 diagonals
There are n vertices.
But if you go around, you have drawn each diagonal from both ends, counting it twice.