Federated learning, an emerging machine learning paradigm, enables clients to collaboratively train a model without exchanging local data. Clients participating in the training process significantly impact the convergence rate, learning efficiency, and model generalization. We propose a novel approach, client filtering, to improve model generalization and optimize client participation and training. The proposed method periodically filters available clients to identify a subset that maximizes a combinatorial objective function with an efficient greedy filtering algorithm. Thus, the clients are assessed as a combination rather than individually. We theoretically analyze the convergence of federated learning with client filtering in heterogeneous settings and evaluate its performance across diverse vision and language tasks, including realistic scenarios with time-varying client availability. Our empirical results demonstrate several benefits of our approach, including improved learning efficiency, faster convergence, and up to 10% higher test accuracy than training without client filtering.