For n states and m input alphabets we can have the formula:

$n*n^{nm}*2^{n}$

=$n^{mn+1}*2^{n}$

In a $DFA$ there might not be a difference if start state changes- as states are unlabeled usually. In such a case, we can divide the above by number of states giving $ n^{mn}×2^{n}$ possible $DFAs$.