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Here we have a set with $n$ elements (e.g.: $A=\{1, 2, 3,\cdots.n\}$), and we want to draw $k$ samples from the set such that ordering matters and repetition is allowed. For example, if $A=\{1,2,3\}$ and $k=2$, there are $9$ different possibilities:

1. (1,1);
2. (1,2);
3. (1,3);
4. (2,1);
5. (2,2);
6. (2,3);
7. (3,1);
8. (3,2);
9. (3,3).

In general, we can argue that there are $k$ positions in the chosen list: $($Position $1$, Position $2$, ..., Position $k)$. There are $n$ options for each position. Thus, when ordering matters and repetition is allowed, the total number of ways to choose $k$ objects from a set with $n$ elements is $$n \times n \times ... \times n=n^k$$ Note that this is a special case of the multiplication principle where there are $k$ "experiments" and each experiment has $n$ possible outcomes.

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