Suppose if I have a lock, in which there are 8 different numbers. The numbers are allowed the repeat. I'm wondering how many possible combinations are there for the lock?
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For each position you have 8 possibilities and you have 8 position so the answer is $8^8$.
If you have a lock with $n$ positions and $k$ possible numbers then the answer would be $k^n$.
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Or $(\overline{10})^n$ in base $k$. – zwim Nov 16 '19 at 20:11