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 ^{N1}/(N1)!
How does this affect your comment?
Update: Oops, I was mistaken.
QM

Quantum Mechanics: The dreams stuff is made of
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