'''simple docstring'''

from math import factorial
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):

 # 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(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'''

def 			__UpperCamelCase       (   UpperCAmelCase = 1		,     UpperCAmelCase = 1000     ):
 lowercase__				:    Dict  =					1
 lowercase__				:    Dict  =					0

 for divide_by_number in range(UpperCAmelCase		,     digit + 1     ):
  lowercase__				:    list[int]  =					[]
  lowercase__				:    Union[str, Any]  =					numerator
  for _ in range(1		,     digit + 1     ):
   if now_divide in has_been_divided:
    if longest_list_length < len(UpperCAmelCase     ):
     lowercase__				:    Dict  =					len(UpperCAmelCase     )
     lowercase__				:    Optional[Any]  =					divide_by_number
   else:
    has_been_divided.append(UpperCAmelCase     )
    lowercase__				:    int  =					now_divide * 10 % divide_by_number

 return the_digit


# Tests
if __name__ == "__main__":
  import doctest

  doctest.testmod()

