Running a randomized algorithm on a subsampled dataset instead of the entire dataset amplifies differential privacy guarantees. In this work, in a federated setting, we consider random participation of the clients in addition to subsampling their local datasets. Since such random participation of the clients creates correlation among the samples of the same client in their subsampling, we analyze the corresponding privacy amplification via non-uniform subsampling. We show that when the size of the local datasets is small, the privacy guarantees via random participation is close to those of the centralized setting, in which the entire dataset is located in a single host and subsampled. On the other hand, when the local datasets are large, observing the output of the algorithm may disclose the identities of the sampled clients with high confidence. Our analysis reveals that, even in this case, privacy guarantees via random participation outperform those via only local subsampling.