


"""simple docstring"""







from math import factorial
def _A						(						lowercase	,   lowercase		):







    """simple docstring"""

    # 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'''		)
    return factorial(lowercase		) // (factorial(lowercase		) * factorial(n - k		))


if __name__ == "__main__":
       print(
           """The number of five-card hands possible from a standard""",
           F'fifty-two card deck is: {combinations(5_2, 5)}\n',
       )

       print(
           """If a class of 40 students must be arranged into groups of""",
           F'4 for group projects, there are {combinations(4_0, 4)} ways',
           """to arrange them.\n""",
       )

       print(
           """If 10 teams are competing in a Formula One race, there""",
           F'are {combinations(1_0, 3)} ways that first, second and',
           """third place can be awarded.""",
       )



"""simple docstring"""







def _A						(						lowercase = 2_00_00_00		):







    """simple docstring"""
    a					=[0 for i in range(n + 1		)]
    a					=1
    a					=1

    for i in range(2	,   int(n**0.5		) + 1		):
        if primality_list[i] == 0:
            for j in range(i * i	,   n + 1	,   lowercase		):
                a					=1
    a					=0
    for i in range(lowercase		):
        if primality_list[i] == 0:
            sum_of_primes += i
    return sum_of_primes


if __name__ == "__main__":
       print(F'{solution() = }')