Final answer:
In a freshly formed star cluster, low-mass main sequence stars are the most common, followed by sunlike main sequence stars, brown dwarfs, high-mass main sequence stars, and finally, white dwarfs, which are the least common due to their longer evolutionary timeline.
Step-by-step explanation:
When a large nebula fragments and forms a star cluster, the distribution of stars by mass shortly after formation is typically as follows: low-mass main sequence stars are the most common since they form more frequently and have longer lifespans.
Next in frequency are sunlike main sequence stars, followed by brown dwarfs. High-mass main sequence stars are less common because they are rarer and they evolve rapidly away from the main sequence stage. Lastly, white dwarfs would be the least common as it takes a significant amount of time for stars to evolve into this final stage, and a newly formed cluster would not yet have many, if any, white dwarfs.
We determine the relative ages of star clusters by observing the types of stars they contain and their positions on the Hertzsprung-Russell (H-R) diagram. The main-sequence turnoff point indicates the mass of stars that are just leaving the main sequence to become red giants, giving an indication of the cluster's age.
Stars with higher masses evolve faster, so a cluster with neutron stars is older than one with only white dwarfs, as the former are the remnants of more massive stars that have ended their life cycle even beyond the white dwarf stage.