Why there are the same number of subsets?

Question

Given a set with 7 elements. Explain why there are the same number of subsets with 2 elements as there are subsets with 5 elements

Answer 1

Because 2 + 5 = 7

You can choose sets of 2 elements in two ways.

1. Choose sets of 2 elements directly.
2. Choose sets of 5 elements, then choose the 2 elements not included in these sets.

In both cases you are going to end up with the same sets of 2 elements, therefore the number of subsets with 2 elements must be the same as the number with 5 because in (2) there is a 1-1 correspondence between a subset with 5 elements and a subset with 2