GRE Permutation and geometry question?

Question

How many heptagons can be drawn by joining the vertices of a polygon with 10 sides?

Answer 1

Label each of the ten vertices with a letter or number, let's say, A - J. Now if you take any 7 of those ten vertices, and draw lines to connect them, you have a unique heptagon. Therefore, the question is really asking: how many ways can you choose 7 letters out of 10 letters. This is the combination formula (order doesn't matter - the shape looks the same no matter what order you make the lines as long as you are connecting the same vertices). So the answer is 10 C 7 = 120