THE FEUTEX TOOLKIT

No-Fixed-Point Assignment Count

Count assignments with no item in its original position and calculate their random-permutation probability.

Probability workspace● Runs in your browser

01 Your input

Distinct objectscount

02 Your result

View or copy raw result data

Result data

Formula

Derangements = round(((n>=2?2:1)*(n>=3?3:1)*(n>=4?4:1)*(n>=5?5:1)*(n>=6?6:1)*(n>=7?7:1)*(n>=8?8:1)*(n>=9?9:1)*(n>=10?10:1)*(n>=11?11:1)*(n>=12?12:1)*(n>=13?13:1)*(n>=14?14:1)*(n>=15?15:1)*(n>=16?16:1)*(n>=17?17:1)*(n>=18?18:1))/E); Probability = round(((n>=2?2:1)*(n>=3?3:1)*(n>=4?4:1)*(n>=5?5:1)*(n>=6?6:1)*(n>=7?7:1)*(n>=8?8:1)*(n>=9?9:1)*(n>=10?10:1)*(n>=11?11:1)*(n>=12?12:1)*(n>=13?13:1)*(n>=14?14:1)*(n>=15?15:1)*(n>=16?16:1)*(n>=17?17:1)*(n>=18?18:1))/E)/((n>=2?2:1)*(n>=3?3:1)*(n>=4?4:1)*(n>=5?5:1)*(n>=6?6:1)*(n>=7?7:1)*(n>=8?8:1)*(n>=9?9:1)*(n>=10?10:1)*(n>=11?11:1)*(n>=12?12:1)*(n>=13?13:1)*(n>=14?14:1)*(n>=15?15:1)*(n>=16?16:1)*(n>=17?17:1)*(n>=18?18:1))

Sources and model references

https://mathworld.wolfram.com/Derangement.html

Worked example

Inputs

Distinct objects: 5 count

Expected results

Derangements: 44 count
Probability: 0.3666666667 probability

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

Enter the labeled inputs using consistent units.
Check the stated assumptions and calculate.
Review each output and compare another input scenario.

Try this example

{
  "n": 5
}

Accuracy and scope

Uniform random permutations of distinct objects; count rounded from n!/e, valid for n≥1. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.