TheAlgorithms/Python · error · ValueError

Please enter positive integers for n and k where n >= k

Error message

Please enter positive integers for n and k where n >= k

What it means

Raised by combinations() in maths/combinations.py when asked for a binomial coefficient that would require a factorial of a negative number: specifically n < k or k < 0. The multiplicative formula res *= n - i over range(k) only makes combinatorial sense for 0 <= k <= n, so the function guards that up front with ValueError.

Source

Thrown at maths/combinations.py:36

    >>> combinations(20,5)
    15504

    >>> combinations(52, 5)
    2598960

    >>> combinations(0, 0)
    1

    >>> combinations(-4, -5)
    ...
    Traceback (most recent call last):
    ValueError: Please enter positive integers for n and k where n >= k
    """

    # If either of the conditions are true, the function is being asked
    # to calculate a factorial of a negative number, which is not possible
    if n < k or k < 0:
        raise ValueError("Please enter positive integers for n and k where n >= k")
    res = 1
    for i in range(k):
        res *= n - i
        res //= i + 1
    return res


if __name__ == "__main__":
    print(
        "The number of five-card hands possible from a standard",
        f"fifty-two card deck is: {combinations(52, 5)}\n",
    )

    print(
        "If a class of 40 students must be arranged into groups of",
        f"4 for group projects, there are {combinations(40, 4)} ways",
        "to arrange them.\n",
    )

View on GitHub (pinned to f5988cc097)

Solutions

1. Check the argument order — the signature is combinations(n, k) with n total items and k chosen.
2. Clamp k with k = min(k, n) or return 0 by convention when k > n, mirroring math.comb.
3. Prefer the standard library math.comb(n, k) which returns 0 for k > n instead of raising.

Example fix

# before
combinations(3, 5)  # ValueError

# after
from math import comb
result = comb(3, 5)  # 0, no exception
# or guard: n, k = max(n, k), min(n, k) if args may be swapped

if k < 0 or n < k:
    raise ValueError(f'need 0 <= k <= n, got n={n}, k={k}')
result = combinations(n, k)

try:
    result = combinations(n, k)
except ValueError:
    result = 0  # mirror math.comb convention for k > n, if that suits your domain

When it happens

Trigger: Calling combinations(-4, -5), combinations(3, 5) (k > n), or combinations(10, -1). Note combinations(0, 0) is valid and returns 1, and combinations(n, 0) returns 1.

Common situations: Swapped arguments (combinations(k, n)); loop bounds where the upper index comes from a shorter list than the selection size (e.g. choosing 5 items from a 3-item list); negative k from subtracting sizes (len(a) - len(b) when b is longer).

Related errors

• Both points must have the same dimension.
• Monogons and Digons are not polygons in the Euclidean space
• All values must be greater than 0
• Undefined for non-natural numbers
• Please enter a valid number

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/875a81a1f8e30cc7. Report an issue: GitHub.