Suppose the final result of a football match is 5:4 to the home team

in order to ensure the A team is always in lead, we need to have first 2 wins by A only. and Last match is to be won by B only because if it is won by A, then that means prior to that game score would be 4:4 and as such team A was not in lead. this fixes first 2 places as A and last place as B.

out of 9 places, 3 places are fixed. now we can start setting combinations. for remaining 6 places, we can only have 3 As and 3Bs. since we already have 2As and 1B in fixed position. in order to get 5 A and 4 B , we need exactly 3 more A and 3 more B.

our basic case for those 6 positions will be AAABBB. i wi send photos of remaining valid cases.

https://drive.google.com/file/d/1nVGFnNMVKbrHDzMVUSptNTkkDlGhQZy_/view?usp=drivesdk