How to find mean distance between galaxies from redshif?

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SUMMARY

To find the mean distance between galaxies at a given redshift, one must utilize the mean number density of galaxies, the redshift (z), and the Hubble constant (H0). The redshift indicates the expansion of the universe and provides a ratio of distances at different times. Understanding the relationship between redshift and Hubble's law is crucial, as it helps in calculating the mean separation between galaxies based on their density and the expansion rate of the universe.

PREREQUISITES
  • Understanding of redshift (z) in cosmology
  • Familiarity with Hubble's law and the Hubble constant (H0)
  • Knowledge of mean number density of galaxies
  • Basic principles of cosmic expansion
NEXT STEPS
  • Research the mathematical relationship between redshift and distance in cosmology
  • Study Hubble's law in detail, including its implications for galaxy distances
  • Explore methods for calculating mean number density of galaxies
  • Investigate cosmic expansion models and their impact on galaxy separation
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Astronomers, astrophysicists, and students studying cosmology who are interested in understanding galaxy distances and the implications of cosmic expansion.

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If we know the mean number density of galaxies in the universe, the redshift z and the Hubble constant. Is it possible to find the mean distance between galaxies at such redshift?

The redshift gives a ratio of two distances between the same pair of bodies, at two different time due to the expansion of the universe. I don't understand how is this parameter related to the mean distance between galaxies. And how is it related to Hubble's law anyway?

The question is attached. All 3 parts are confusing me...Please show some approaching ideas or solution, thank you!
 

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If you know the mean number density, what else do you need to know in order to work out the mean separation?
 

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