**Core Concept**
Cluster sampling is a type of probability sampling where the population is divided into clusters or groups, and a random selection of these clusters is chosen for the study. This method is often used when the population is dispersed or when the sampling frame is not available.

**Why the Correct Answer is Right**
In this scenario, the region is divided into 50 villages, which serve as the clusters. A random selection of 10 villages is chosen for the study, indicating that cluster sampling is the appropriate method. This type of sampling is particularly useful when the clusters are already defined and easily identifiable, such as villages or neighborhoods. The random selection of villages allows for a representative sample of the population, making it a reliable method for estimating population parameters.

**Why Each Wrong Option is Incorrect**
**Option A:** Simple Random sampling involves selecting individual units (e.g., villages) randomly from the population, rather than selecting a random subset of clusters. This is not the case in the given scenario.
**Option B:** Stratified sampling involves dividing the population into distinct subgroups (strata) and sampling from each stratum separately. The villages in this scenario are not divided into distinct subgroups, making stratified sampling not applicable.
**Option D:** Systematic Sampling involves selecting individual units at fixed intervals from the population. This method does not involve selecting clusters, making it not relevant to the given scenario.

**Clinical Pearl / High-Yield Fact**
When using cluster sampling, it's essential to ensure that the selected clusters are representative of the population and that the sample size is sufficient to produce reliable estimates.

**Correct Answer:**
✓ Correct Answer: C. Cluster Sampling