Which cluster is known for its high density and large number of stars?

The correct choice is the globular cluster, which is characterized by its high density of stars and its large number of members, often containing hundreds of thousands to millions of stars. Globular clusters are tightly bound by gravity, which contributes to their compact structure and high density. They are typically found in the halos of galaxies and are among the oldest stellar formations, with ages often exceeding 10 billion years.

In contrast, open clusters, while also containing groups of stars, are usually less dense and contain fewer stars, often just hundreds to a few thousand. Binary stars consist of pairs of stars orbiting each other and lack the collective density characteristic of clusters, while eclipsing binaries refer specifically to a type of binary star system in which one star periodically blocks the light from another, and are not clusters at all. Thus, the defining features of globular clusters make them the clear answer in this context.