Reference request: Set of n-Multisets of elements in $\mathbb{N}$ is countable set

Question

Let $n \in \mathbb{N}$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $\mathbb{N}$ \begin{equation} M_{\mathbb{N}} = \{ \{a_1, ..., a_n\} \mathrm{~is~multiset}| a_i \in \mathbb{N} \} \end{equation} is a set and is countable.

Answer 1

There is a bijection $\mathcal{M}_{\mathbb{N}} \rightarrow \bigcup_{k=0}^{\infty}\mathbb{N}^k$. Now each $\mathbb{N}^k$ is countable and countable unions of countable sets are again countable.