Get the number of permutations in Python: Calculate nPk (the number of ways to choose and order items)

The perm() in math module returns the number of patterns to choose k objects from n objects and order them, that is _nP_k.

math.perm(n, k=None)

The method is available from Python 3.8. The first argument is the number of total items and the second is the number of items you choose and order.

Example

Here is the examples of choosing 0 to 5 items from 5 items and ordering.

import math

p0 = math.perm(5, 0)
p1 = math.perm(5, 1)
p2 = math.perm(5, 2)
p3 = math.perm(5, 3)
p4 = math.perm(5, 4)
p5 = math.perm(5, 5)

print(p0, p1, p2, p3, p4, p5)
# 1 5 20 60 120 120

Choosing 2 items from 5 items with order has 20 ways.

perm(5, 2) = ₅P₂ = 5 × 4 = 20

In case k is not specified

p = math.perm(5)
print(p)  # 120

The math.perm(5) and math.perm(5, 5) are equivalent and both are equal to 5! = 120.