



"""simple docstring"""






from math import factorial


def     _lowercase       (						__snake_case      ,__snake_case			):



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






import math


def     _lowercase       (						__snake_case      ,__snake_case			)		->     float:
			return math.pow(__snake_case      ,2			) - a


def     _lowercase       (						__snake_case			)		->     float:
			return 2 * x


def     _lowercase       (						__snake_case			)		->     float:
			__lowerCAmelCase   :						List[str]				= 2.0

			while start <= a:
						__lowerCAmelCase   :						Union[str, Any]				= math.pow(__snake_case      ,2			)

			return start


def     _lowercase       (						__snake_case      ,__snake_case = 9_999      ,__snake_case = 0.00000000000001			)		->     float:

			if a < 0:
						raise ValueError("math domain error"			)

			__lowerCAmelCase   :						List[Any]				= get_initial_point(__snake_case			)

			for _ in range(__snake_case			):
						__lowerCAmelCase   :						Union[str, Any]				= value
						__lowerCAmelCase   :						List[str]				= value - fx(__snake_case      ,__snake_case			) / fx_derivative(__snake_case			)
						if abs(prev_value - value			) < tolerance:
									return value

			return value


if __name__ == "__main__":
	from doctest import testmod

	testmod()