Permutation With Repetition Calculator

Work out permutation with repetition instantly with clear inputs, formula shown and shareable results.

About Permutation With Repetition Calculator

When repetition is allowed each of the r positions can independently take any of the n values, giving nʳ arrangements. Forbidding repeats reduces the choices at each step, giving n(n−1)…(n−r+1).

Formulas

With repetition

nʳ

Without repetition

P(n, r) = n!/(n − r)!

Worked example

With the default values below, Permutation With Repetition Calculator returns Arrangements allowing repeats of 10,000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Items to choose fromaccepts 1–300: 10
Positions to fillaccepts 1–300: 4

Results

Arrangements allowing repeats: 10,000
Arrangements without repeats: 5,040
How many times more with repeats: 1.984127
Bits of information: 13.287712

Step by step

1Values used
2With repetition
3Without repetition
4Arrangements allowing repeats= 10,000
5Arrangements without repeats= 5,040
6How many times more with repeats= 1.984127
7Bits of information= 13.287712

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How many 4-digit PINs are there?

10⁴ = 10000 with repeats allowed, but only 5040 if every digit must differ.

Why report bits?

log₂ of the count is the entropy in bits, which is the standard way to quantify password or key strength.