clrs Exercise 5.3-3

Suppose that instead of swapping element A[i]$A[i]$ with a random element from the subarray A[i…n]$A[i \ldots n]$, we swapped it with a random element from anywhere in the array:

PERMUTE-WITH-ALL(A)
n = A.length
for i = 1 to n
    swap A[i] with A[RANDOM(1,n)]

Does this code produce a uniform random permutation? Why or why not?

Of course, this is a popular problem and there are tons of posts and papers written on it. Here's one from Coding Horror