The multi-stage cluster sample is most helpful when

Multi-stage cluster sampling is most helpful across all three conditions listed, so all of the above holds.

Wide geographical dispersion of the population is one strong reason to use it.

Time and money constraints on the researcher are a second reason it is chosen.

Wanting a probability sample for generalizing the results is a third supporting reason.

It selects clusters in successive stages, sampling smaller units within larger ones.

Costs fall because fieldwork concentrates within the finally selected clusters.