

import qiskit



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase					)							->     qiskit.result.counts.Counts:



  """simple docstring"""






  _snake_case						=							qiskit.Aer.get_backend('''aer_simulator'''					)

  _snake_case						=							qiskit.QuantumCircuit(4			,	2					)
  # encode inputs in qubits 0 and 1
  if bita == 1:
    qc_ha.x(0					)
  if bita == 1:
    qc_ha.x(1					)
  qc_ha.barrier()

  # use cnots to write XOR of the inputs on qubit2
  qc_ha.cx(0			,	2					)
  qc_ha.cx(1			,	2					)

  # use ccx / toffoli gate to write AND of the inputs on qubit3
  qc_ha.ccx(0			,	1			,	3					)
  qc_ha.barrier()

  # extract outputs
  qc_ha.measure(2			,	0					)  # extract XOR value
  qc_ha.measure(3			,	1					)  # extract AND value

  # Execute the circuit on the qasm simulator
  _snake_case						=							qiskit.execute(_UpperCamelCase			,	_UpperCamelCase			,	shots=1_000					)

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


if __name__ == "__main__":
 __A      		=     half_adder(1, 1)
 print(f'''Half Adder Output Qubit Counts: {counts}''')




from math import factorial



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase					)							->     int:



  """simple docstring"""






  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.''',
 )

