Derangement Probability

Problem

The probability that a uniform random permutation of n items has no fixed point is !n / n!, where !n is the derangement count with !0 = 1 and !n = (n - 1)(!(n-1) + !(n-2)).

Given n, return the probability.

Hint

The probability approaches 1/e as n grows.

Test cases

case 1

in: [3]

expected: 0.3333333333333333

case 2

in: [4]

expected: 0.375

case 3

in: [5]

expected: 0.36666666666666664

Starter codePython

def derangement_probability(n):
    # Your code here
    pass

3 test cases · run your code against them in the editor