- (i)
- ; there exists only one possibility to choose 0 element from a set (you don't choose anything!).
- (ii)
- ; you have different choices for a single element.

- ;
- .

- We replace into the definition:

- We begin from the right-hand side:

and so on. Compare the coefficients of these developments (together with the coeeficients in and ) with the rows of Pascal's triangle).

- For , the equality is trivial.
- Assume that for some natural number , the equality holds. Then we have: