






"""simple docstring"""
from math import factorial






def       __UpperCamelCase						(		snake_case__ , snake_case__       ):

	# 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(snake_case__       ) // (factorial(snake_case__       ) * 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"""
from __future__ import annotations






def       __UpperCamelCase						(		snake_case__ , snake_case__       ):
	if len(snake_case__       ) == 0:
		return False
	A_		:    Union[str, Any]						     = len(snake_case__       ) // 2
	if a_list[midpoint] == item:
		return True
	if item < a_list[midpoint]:
		return binary_search(a_list[:midpoint] , snake_case__       )
	else:
		return binary_search(a_list[midpoint + 1 :] , snake_case__       )


if __name__ == "__main__":
							_lowerCAmelCase       =				input("Enter numbers separated by comma:\n").strip()
							_lowerCAmelCase       =				[int(item.strip()) for item in user_input.split(",")]
							_lowerCAmelCase       =				int(input("Enter the number to be found in the list:\n").strip())
							_lowerCAmelCase       =				"" if binary_search(sequence, target) else "not "
							print(F'{target} was {not_str}found in {sequence}')

