Function combinations

maths/combinations.py:6–41

Returns the number of different combinations of k length which can be made from n values, where n >= k. Examples: >>> combinations(10,5) 252 >>> combinations(6,3) 20 >>> combinations(20,5) 15504 >>> combinations(52, 5) 2598960 >>> combinations(0,

(n: int, k: int)

def combinations(n: int, k: int) -> int:
    """
    Returns the number of different combinations of k length which can
    be made from n values, where n >= k.

    Examples:
    >>> combinations(10,5)
    252

    >>> combinations(6,3)
    20

    >>> 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__":