A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation. A good example of a random permutation is the shuffling of a deck of cards: this is ideally a random permutation of the 52 cards. Generating random permutations Entry-by-entry brute force method One method of generating a random permutation of a set of length n uniformly at random (i.e., each of the n! permutations is equally likely to appear) is to generate a sequence by taking a random number between 1 and n sequentially, ensuring that there is no repetition, and interpreting this sequence (x1, ..., xn) as the permutation shown here in two-line notation. This brute-force method will require occasional retries whenever the random number picked is a repeat of a number already selected. This can be avoided if, on the ith step (when x1, ..., xi − 1 have already been chosen), one chooses a number j at random between 1 and n − i + 1 and sets xi equal to the jth largest of the unchosen numbers. Fisher-Yates shuffles A simple algorithm to generate a permutation of n items uniformly at random without retries, known as the Fisher–Yates shuffle, is to start with any permutation (for example, the identity permutation), and then go through the positions 0 through n − 2 (we use a convention where the first element has index 0, and the last element has index n − 1), and for each position i swap the element currently there with a randomly chosen element from positions i through n − 1 (the end), inclusive. It's easy to verify that any permutation of n elements will be produced by this algorithm with probability exactly 1/n!, thus yielding a uniform distribution over all such permutations. unsigned uniform(unsigned m); /* Returns a random integer 0 <= uniform(m) <= m-1 with uniform distribution */ void initialize_and_permute(unsigned permutation[], unsigned n) { unsigned i; for (i = 0; i <= n-2; i++) { unsigned j = i+uniform(n-i); /* A random integer such that i ≤ j < n */ swap(permutation[i], permutation[j]); /* Swap the randomly picked element with permutation[i] */ } } Note that if the uniform() function is implemented simply as random() % (m) then a bias in the results