In like manner the same state can be realized by many other such complexions. The desired number of all possible complexions can be found by considering the digit row designated above by (15). For, since the number of molecules (dice) is given, the digit row will have a particular number of places (
). Besides, since the number of molecules belonging to each elementary space is given, each digit will occur equally often in the row in all permissible complexions. Moreover every change in digit arrangement effects a new complexion. The number of the possible complexions or the probability
of the given state is therefore equal, under the conditions specified, to the possible "permutations with repetition."[21] In the simple example chosen we have for such permutation, according to a known formula,
Consequently in the general case, we have
where the sign