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 NN for any N > 1, but more importantly, it is not a divisor of NN, which means that it is impossible for the algorithm to give equal weight to all the permutations.
If I'm not mistaken, N! | NN
, as N! = 1*2*...*N, and NN
= N*N*...*N. Therefore, NN
/N! = NN-1
How does this affect your comment?
Update: Oops, I was mistaken.
Quantum Mechanics: The dreams stuff is made of