
"""simple docstring"""




import math

lowercase  : Dict						   =							10
lowercase  : Dict						   =							7
lowercase  : str						   =							BALLS_PER_COLOUR * NUM_COLOURS







def 						_snake_case(  SCREAMING_SNAKE_CASE__ = 20    )			->   List[Any]:
       lowercase							:					int	     =				math.comb(a_ ,     a_    )
       lowercase							:					Tuple	     =				math.comb(NUM_BALLS - BALLS_PER_COLOUR ,     a_    )

       lowercase							:					Union[str, Any]	     =				NUM_COLOURS * (1 - missing_colour / total)

       return f"{result:.9f}"


if __name__ == "__main__":
  print(solution(20))


from __future__ import annotations

import numpy as np







def 						_snake_case(  SCREAMING_SNAKE_CASE__    )			->   tuple[np.ndarray, np.ndarray]:
       lowercase     ,      lowercase							:					Dict	     =				np.shape(SCREAMING_SNAKE_CASE__    )
       if rows != columns:
              lowercase							:					str	     =				(
                  """'table' has to be of square shaped array but got a """
                  f"{rows}x{columns} array:\n{table}"
              )
              raise ValueError(SCREAMING_SNAKE_CASE__    )

       lowercase							:					Any	     =				np.zeros((rows, columns)    )
       lowercase							:					int	     =				np.zeros((rows, columns)    )
       for i in range(SCREAMING_SNAKE_CASE__    ):
              for j in range(SCREAMING_SNAKE_CASE__    ):
                     lowercase							:					Optional[int]	     =				sum(lower[i][k] * upper[k][j] for k in range(SCREAMING_SNAKE_CASE__    )    )
                     if upper[j][j] == 0:
                            raise ArithmeticError("""No LU decomposition exists"""    )
                     lowercase							:					str	     =				(table[i][j] - total) / upper[j][j]
              lowercase							:					Optional[Any]	     =				1
              for j in range(SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    ):
                     lowercase							:					Any	     =				sum(lower[i][k] * upper[k][j] for k in range(SCREAMING_SNAKE_CASE__    )    )
                     lowercase							:					Tuple	     =				table[i][j] - total
       return lower, upper


if __name__ == "__main__":
  import doctest

  doctest.testmod()
