Sudoku solutiuons mathematics

How many unique sudoku solutions is there? How do one calculate it?

Besides, can every sudoku be generated by applying this technique (now they have forgotten to shuffel the different sets of alike digits with each other)? Or is there some solutions that will NEVER be produced? Is there equal chanse to produce every one of them?

Well, it's a tricky problem but there must be some way to calculate it. I have been thinking of creating a sudoku generator and I'm choosing between that method and bruteforcing a sulotion included making guesses and backtracking. That will produce every solution with equal chanses, but it's much slover.

Thanks