The size of this sample space is NN. To each element of this space corresponds a permutation, but the size of the space of all possible permutations is N! , which is not only smaller than N^{N} for any N > 1, but more importantly, it is not a divisor of N^{N}, which means that it is impossible for the algorithm to give equal weight to all the permutations.
If I'm not mistaken, N! | N
^{N}, as N! = 1*2*...*N, and N
^{N} = N*N*...*N. Therefore, N
^{N}/N! = N
^{N-1}/(N-1)!
How does this affect your comment?
Update: Oops, I was mistaken.
-QM
--
Quantum Mechanics: The dreams stuff is made of