Function or Combinatorics?

Let $f: \mathbb{Z^+} \times \mathbb{Z^+} \to \mathbb{N}$ be a function such that

$\large f(m,n)={m \choose n}$

where $n \leq m$ .

Then which of the following statement(s) regarding $f$ is/are true?

A: $f$ is a bijective function .
B: $f$ is a many-to-one function.
C: $f$ is an onto function.
D: $f$ is a one-to-one function.
E: $f$ is a one-to-many function.

Put 1 for a correct option, and 9 for an incorrect one. For example, if all five are correct, then enter 11111.