I read that William had 300 knights that were direct vassals under him. Even if each knight brought 6 friends thats only an army of 1800 men. So how did he raise around 8000-10,000 soldiers?
Also bonus question what was the population of Normandy during this period? I cant find information on this anywhere.
I think /u/Rittermeister 's answer here is a good place to start, though there's always more to say on any topic.