






"""simple docstring"""

from math import factorial






def _lowerCAmelCase	(  __lowerCamelCase:int ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						if n < k or k < 0:
												raise ValueError("Please enter positive integers for n and k where n >= k"   )
						return factorial(__lowerCamelCase   ) // (factorial(__lowerCamelCase   ) * factorial(n - k   ))


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''',
			)

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











"""simple docstring"""

def _lowerCAmelCase	(  __lowerCamelCase:int = 2_0_0_0_0_0_0   ):

						'''simple docstring'''






						__magic_name__            =     [0 for i in range(n + 1   )]
						__magic_name__            =     1
						__magic_name__            =     1

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


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



