Eugene Salamin <gene_salamin@yahoo.com> wrote:

Here is one way to generate derangements with equal probability. Place numbers 2 to n in a hat. Draw a number; it becomes p(1). Put 1 into the hat and withdraw 2 if it is not p(1). Draw a number; it becomes p(2). Replace 2 if it is not p(1), and withdraw 3 if it is not p(1) or p(2). Draw a number; it becomes p(3). And so on.

I think you can derange 1,...,n-1 and have nothing to pick for p(n). Dan