Settlers of Catan Boards possibilities I wanted to calculate the number of possible boards exists in normal settlers of catan board game. I would like someone to approve me me my calcuations are correct or I might counts possibilities more than one time.
so there are 12 outside tiles 6 in the middle and 1 in the center.
I want to choose fist 12 to be in the the outer circle:
19 over 12 (nCr), now I want to order them between them selves that would be 11! (for a circle with n elements there are (n-1)! possibles ways to order it)
now then same for the middle circle only now it would be 7 over 6 because we used 12 already for the outer circle and here it would be 5! to order the middle circle and the last circle in the middle well there is only 1 left so no need to count it.
sense we have tiles that repeat them selfs:
A-4, B-4, C-4, D-3, E-3
so I got to ((19 choose 12) * 11! * (7 choose 6) * 5!)/(4!*4!*4!*3!*3!))
what do you guys think?

There are 19 tiles, which gives 19! permutations.
But, some are repeated resources. There are 4 sheep, wood and grain and 3 ore and brick. So we divide by 4!*4!*4!*3!*3! (=497664) to counter that.
The orientation of the board can also be in 12 different directions which means we overcounted. So we must divide by 12.
121,645,100,408,832,000 / (4!*4!*4!*3!*3!*12) =
121,645,100,408,832,000 / 5,971,968 =
20,369,349,000
