Question

Are the stars in a star cluster, such as the Pleiades, physically associated with each other? Is it likely that, just by chance, a large number of stars appear to be in almost the same direction in the sky, but are in fact at very different distances from the Earth?

Answer 1

Pleiades is an open cluster.

Open clusters are physically related groups of stars held together by mutual gravitational attraction. Open clusters populate about the same regions of the Milky Way and other galaxies as diffuse nebulae, and are found along the band of the Milky Way in the sky.

So, yes the stars in a star cluster, such as the Pleiades, are physically associated with each other.

Again it is also possible that a large number of stars appear to be in almost the same direction in the sky, but are in fact at very different distances from the Earth. This happens in the case of globular clusters.

Globular clusters are gravitational bound concentrations of approximately ten thousand to one million stars, spread over a volume of several tens to 200 light years in diameter.