Permutations with repetitions

Permutations with repetitions is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Permutations with repetitions is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Generate a sequence of permutations of n elements drawn from choice of k values.

This sequence will have $n^{k}$ elements, unless the program decides to terminate early.

Do not store all the intermediate values ion the sequence, rather generate them as required, and pass the intermediate result to a deciding routine.

For example: When "cracking" a "combination" lock a sequence is required, but the sequence is terminated once a successful "combination" is found. This case is a good example of where it is not required to store all the intermediate 'permutations.

See Also:

The number of samples of size k from n objects.

With   combinations and permutations   generation tasks.

	Order Unimportant	Order Important
Without replacement	${\binom {n}{k}}=^{n}\operatorname {C} _{k}={\frac {n(n-1)\ldots (n-k+1)}{k(k-1)\dots 1}}$	$^{n}\operatorname {P} _{k}=n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)$
	Task: Combinations	Task: Permutations
With replacement	${\binom {n+k-1}{k}}=^{n+k-1}\operatorname {C} _{k}={(n+k-1)! \over (n-1)!k!}$	$n^{k}$
	Task: Combinations with repetitions	Task: Permutations with repetitions