> [!NOTE] Lemma > The number of ways to place $k$ labelled balls into $n$ labelled boxes is $n^k$ (the cardinality of $\{ f: [n] \to [k] \}$, where $[n]=\{ 1, 2, \dots,n \}$) equals $n^k$. ###### Proof Follows from [[Product Rule for Counting (Fundamental Counting Principle)]].