
"""simple docstring"""







from math import factorial
def    __lowerCAmelCase    (_UpperCamelCase	,  _UpperCamelCase		):





	if n < k or k < 0:
		raise ValueError('Please enter positive integers for n and k where n >= k'		)
	return factorial(_UpperCamelCase		) // (factorial(_UpperCamelCase		) * 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 qiskit
def    __lowerCAmelCase    (_UpperCamelCase	,  _UpperCamelCase		):
	__lowerCAmelCase      :						Union[str, Any]						      =				qiskit.Aer.get_backend('aer_simulator'		)

	# Create a Quantum Circuit acting on the q register
	__lowerCAmelCase      :						str						      =				qiskit.QuantumCircuit(_UpperCamelCase	,  _UpperCamelCase		)

	# Map the quantum measurement to the classical bits
	circuit.measure([0]	,  [0]		)

	# Execute the circuit on the simulator
	__lowerCAmelCase      :						Optional[int]						      =				qiskit.execute(_UpperCamelCase	,  _UpperCamelCase	,  shots=1000		)

	# Return the histogram data of the results of the experiment.
	return job.result().get_counts(_UpperCamelCase		)


if __name__ == "__main__":
							print(f'Total count for various states are: {single_qubit_measure(1, 1)}')