In this paper, we study the convergence of Federated Averaging (FedAvg) with partial participation under a general variance condition. In each communication round, the server samples $S$ of the $n$ clients uniformly at random without replacement. The stochastic gradients are assumed to satisfy the so-called ABC condition, which allows their variance to grow with the local objective gaps. For smooth nonconvex objectives, we establish a finite-time stationarity bound in terms of the heterogeneity measure $σ_f^\star:=f^\star-\frac{1}{n}\sum_{i=