1.2.3 Permutations with Unlimited Repetition

Consider the selection of $k$ objects from as set of $n$ objects where order matters and repetition is allowed.
Any such selection is called a $k$ -permutation with unlimited repetition of a set of $n$ objects

For positive integers $k$ and $n$ , the number of $k$ -permutations with unlimited repetition of a set of $n$ objects is $n^{k}$ ###### Proof
Consider the Multiplication Principle:
If there is unlimited repetition, then for any $i_{m}$ there are $n$ possible outcomes
$∴$ The number of $k$ -permutations with unlimited repetition is $n^{k}$