Let $(X_{n,i})_{1\le i\le n}$ be independent indicator random variables for each $n$, with $\mathbb{P}(X_{n,i}=1)=p_{n,i}$. Set $S_n=\sum_{i=1}^n X_{n,i}$ and $\lambda_n=\sum_{i=1}^n p_{n,i}$. If $\lambda_n\to \lambda>0$ and $\max_{1\le i\le n}p_{n,i}\to 0$, then $S_n \xrightarrow{d} \operatorname{Poi}(\lambda)$.