GRE geometry question?

Question

If you join all the vertices of a heptagon, how many quadrilaterals will you get? Any clues to help me solve the problem.

Answer 1

heptagon has 7 vertices

Need choose 4 out the 7 vertices to form a quadrilateral

Combinatorial

C(7, 4) = 7!/(4! 3!) = 35

Answer 2

A heptagon also has 7 vertices. 

If you choose ANY 4 of the 7 vertices and connect them with lines, you will get a quadrilateral. 

So, the question really becomes "In how many different ways can you select 4 of the 7 vertices?"

Since the order in which we select the 4 vertices does not matter, we can use combinations. 

We can select 4 of the 7 vertices in 7C4 ways

7C4 = 7!/(4!3!)= 35