Help with difficult GRE math question?

Question

I don't understand how to calculate questions like this:

If you join all the vertices of a heptagon, how many quadrilaterals will you get?

A)72

B)36

C)25

D)35

E)120

Can anyone explain how to tackles these types of questions in general?

Answer 1

heptagon = 7-sided polygon.

quadrilateral = 4-sided polygon.

answer

= choose 4 vertices from 7 available

= 7C4

= 7! / 3!4!

= 5*6*7 / 1*2*3

= 35 , choice D.