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It can be but it is not simple random sampling.
They include: Simple random sampling, Systematic sampling, Stratified sampling, Quota sampling, and Cluster sampling.
What I believe you are referring to is cluster sampling or cluster. In cluster sampling, the population is divided into clusters and all population members in the cluster are sampled.
Multistage sampling is a form of cluster sampling where instead of using the entire cluster, random samples from each cluster are used. This is typically used when doing opinion polls or surveys.
simple random, stratified sampling, cluster sampling