Reference · Math

math.perm

math.perm(int, int | null=) -> int

What it does

The number of ways to pick k items from n in order, n! / (n - k)!, as an int, as Python's math.perm: math.perm(5, 2) is 20. Without k, or with k of null, it is n!, all the orderings of n items.

Examples

print(math.perm(5, 2), math.perm(5), math.perm(5, null))print(math.perm(10, 3) == math.comb(10, 3) * math.factorial(3))

20 120 120true

Edge cases

• k greater than n gives 0, not an error.
• k of 0 gives 1; math.perm(0) is 1 as well.
• The result is an int of 64 bits: math.perm(20) fits, math.perm(21) is a runtime error, integer overflow, and so is any n, k pair whose product passes about 9.2 × 10¹⁸. Python's result grows without bound.
• A float that is a whole number is accepted as an int.

print(math.perm(5, 6), math.perm(5, 0), math.perm(0), math.perm(0, 0))print(math.perm(20), math.perm(100, 2), math.perm(6.0, 2))

0 1 1 12432902008176640000 9900 30

print(math.perm(21))

line 1: integer overflow

Errors

A negative n or k is a runtime error, not an error value, with a message that says so, as Python's ValueError. A fraction, text or null for n is a runtime error as well.

print(math.perm(5, -1))

line 1: `math.perm` is not defined for negative numbers (-1)

print(math.perm("5"))

line 1: `math.perm` expects an int as argument 1, got str

Chaining

In a pipeline n comes first, so n | math.perm(k):

print(10 | math.perm(3))print(range(1, 6) | map(math.perm))

720[1, 2, 6, 24, 120]

See also

math.comb, math.factorial, math.prod

Edit this page on GitHub · every example's output was made by running it (tools/refcheck.mjs) · questions on Discord or r/quillo