

'''simple docstring'''






from math import factorial


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



 if n < k or k < 0:
  raise ValueError('''Please enter positive integers for n and k where n >= k'''   )
 return factorial(A__   ) // (factorial(A__   ) * 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 	_A  (					A__ = 50   ):






 """simple docstring"""



 __lowercase													=				[1] * (length + 1)

 for row_length in range(3  ,       length + 1   ):
  for block_length in range(3  ,       row_length + 1   ):
   for block_start in range(row_length - block_length   ):
    ways_number[row_length] += ways_number[
        row_length - block_start - block_length - 1
    ]

   ways_number[row_length] += 1

 return ways_number[length]


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

