

from __future__ import annotations



def 				snake_case_(_UpperCamelCase					)							->     bool:



  """simple docstring"""






  _snake_case						=							str(_UpperCamelCase					)
  return len(_UpperCamelCase					) == 9 and set(_UpperCamelCase					) == set('''123456789'''					)



def 				snake_case_()							->     int | None:



  """simple docstring"""






  for base_num in range(9_999			,	4_999			,	-1					):
    _snake_case						=							100_002 * base_num
    if is_9_pandigital(_UpperCamelCase					):
      return candidate

  for base_num in range(333			,	99			,	-1					):
    _snake_case						=							1_002_003 * base_num
    if is_9_pandigital(_UpperCamelCase					):
      return candidate

  return None


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




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.''',
 )

