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Recently, a new distributed learning scheme called Federated Learning (FL) has been introduced. FL is designed so that server never collects user-owned data meaning it is great at preserving privacy. FL's process starts with the server sending a model to clients, then the clients train that model using their data and send the updated model back to the server. Afterward, the server aggregates all the updates and modifies the global model. This process is repeated until the model converges. This study focuses on an FL setting called cross-device FL, which trains based on a large number of clients. Since many devices may be unavailable in cross-device FL, and communication between the server and all clients is extremely costly, only a fraction of clients gets selected for training at each round. In vanilla FL, clients are selected randomly, which results in an acceptable accuracy but is not ideal from the overall training time perspective, since some clients are slow and can cause some training rounds to be slow. If only fast clients get selected the learning would speed up, but it will be biased toward only the fast clients' data, and the accuracy degrades. Consequently, new client selection techniques have been proposed to improve the training time by considering individual clients' resources and speed. This paper introduces the first availability-aware selection strategy called MDA. The results show that our approach makes learning faster than vanilla FL by up to 6.5%. Moreover, we show that resource heterogeneity-aware techniques are effective but can become even better when combined with our approach, making it faster than the state-of-the-art selectors by up to 16%. Lastly, our approach selects more unique clients for training compared to client selectors that only select fast clients, which reduces our technique's bias.