Hi,
I'm working on a sudoko solver. my method is using a game tree and explore possible permutations for each set of digits by DFS Algorithm.

in order to analyzing problem, i want to know what is the count of possible valid and invalid sudoko tables?

-> a 9*9 table that have 9 one, 9 two, ... , 9 nine.

(this isn't exact duplicate by this question)

my solution is:

1- First select 9 cells for 1s: (*)

2- and like (1) for other digits (each time, 9 cells will be deleted from remaining available cells): C(81-9,9) , C(81-9*2,9) .... =

3- finally multiply the result by 9! (permutation of 123456789 in (*))

this is not equal to accepted answer of this question but problems are equivalent. what did i do wrong?