Number of ways to divide 12 people into 3 teams, where order matters or it does not


New Member
How many ways are there to categorize 12 people into 3 teams of 4?
  • if order does not matter: 12!/4!4!4!3! or ((12 choose 4)(8 choose 4) (4 choose 4))/3!
  • if order matters across teams: 12!/4!4!4! (or (12 choose 4) (8 choose 4) (4 choose 4))
Then, if order matters within teams or if order matters across and within teams, what do we divide 12! by? If order mattered within teams, would we divide by 3! only? What if order mattered across and within teams? It seems we don't divide by anything, but I'm just not sure.

Please help. Thank you so much.