After the course of linear algebra I'm more familiar with vector spaces rather than modules so my question may seem to be silly but I think it's quite natural for someone who thinks of modules as 'vector spaces over a ring': which of the following is free module (free means: having a basis, all of them are over ring $\mathbb{Z}$):

a) $\mathbb{Z}^{\infty}$-all sequences of integers,

b) $\mathbb{Z}^{\mathbb{R}}$-all functions $f: \mathbb{R} \to \mathbb{Z}$,

c) the set of all functions $f: \mathbb{R} \to \mathbb{Z}$ with at most countable support?