This paper introduces a novel backdoor attack called Full Combination Backdoor Attack (FCBA) in federated learning (FL), which outperforms existing methods in terms of attack persistence. FCBA leverages combinatorics to generate diverse local triggers, enabling the global model to learn more robust backdoor patterns. The attack is designed to withstand benign updates, maintaining high attack success rates over multiple iterations. The method is tested on three datasets (MNIST, CIFAR-10, GTSRB) and two model architectures, demonstrating superior performance compared to state-of-the-art backdoor attacks like Distributed Backdoor Attack (DBA). FCBA's persistence is measured through attack success rate (ASR) over rounds, with results showing significantly higher ASR in all datasets. The attack is robust against existing defense mechanisms, including differential privacy and Byzantine tolerance strategies. The paper also analyzes the impact of various factors, such as the scale factor and data distribution, on FCBA's effectiveness. The results highlight the need for improved defenses against persistent backdoor attacks in FL.This paper introduces a novel backdoor attack called Full Combination Backdoor Attack (FCBA) in federated learning (FL), which outperforms existing methods in terms of attack persistence. FCBA leverages combinatorics to generate diverse local triggers, enabling the global model to learn more robust backdoor patterns. The attack is designed to withstand benign updates, maintaining high attack success rates over multiple iterations. The method is tested on three datasets (MNIST, CIFAR-10, GTSRB) and two model architectures, demonstrating superior performance compared to state-of-the-art backdoor attacks like Distributed Backdoor Attack (DBA). FCBA's persistence is measured through attack success rate (ASR) over rounds, with results showing significantly higher ASR in all datasets. The attack is robust against existing defense mechanisms, including differential privacy and Byzantine tolerance strategies. The paper also analyzes the impact of various factors, such as the scale factor and data distribution, on FCBA's effectiveness. The results highlight the need for improved defenses against persistent backdoor attacks in FL.