Variations with repetition

\overline{V}_n^k=n^k

Result unit: — (liczba)

What it describes

The number of k-element sequences chosen from n elements, when elements may repeat.

n

number of elements

k

length of the sequence

For each of the k positions there are the full n possibilities (elements may repeat) — hence

n^k

PIN codes, passwords, license plates (repetition allowed).

How many 3-digit PINs are there (digits 0–9)?

Substitution

n=10

k=3

Result

10^3=1000

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