
'''simple docstring'''

import math

__snake_case:  Dict								=			10
__snake_case:  List[str]								=			7
__snake_case:  int								=			BALLS_PER_COLOUR * NUM_COLOURS






def 	_snake_case						(      A_       :    int = 20   ):
  """simple docstring"""







  a_      :	Dict      =							math.comb(A_     ,		A_   )
  a_      :	List[Any]      =							math.comb(NUM_BALLS - BALLS_PER_COLOUR     ,		A_   )

  a_      :	List[str]      =							NUM_COLOURS * (1 - missing_colour / total)

  return f'''{result:.9f}'''


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




'''simple docstring'''

from typing import List, Optional, TypeVar

from .arrow_dataset import Dataset, _concatenate_map_style_datasets, _interleave_map_style_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .info import DatasetInfo
from .iterable_dataset import IterableDataset, _concatenate_iterable_datasets, _interleave_iterable_datasets
from .splits import NamedSplit
from .utils import logging
from .utils.py_utils import Literal


__snake_case:  Optional[Any]								=			logging.get_logger(__name__)


__snake_case:  Tuple								=			TypeVar("DatasetType", Dataset, IterableDataset)






def 	_snake_case						(      A_       :    List[DatasetType]     ,		A_       :    Optional[List[float]] = None     ,		A_       :    Optional[int] = None     ,		A_       :    Optional[DatasetInfo] = None     ,		A_       :    Optional[NamedSplit] = None     ,		A_       :    Literal["first_exhausted", "all_exhausted"] = "first_exhausted"     ,		):
  """simple docstring"""







  from .arrow_dataset import Dataset
  from .iterable_dataset import IterableDataset

  if not datasets:
    raise ValueError("""Unable to interleave an empty list of datasets."""   )
  for i, dataset in enumerate(A_   ):
    if not isinstance(A_     ,		(Dataset, IterableDataset)   ):
      if isinstance(A_     ,		(DatasetDict, IterableDatasetDict)   ):
        if not dataset:
          raise ValueError(
              f'''Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} '''
              """is an empty dataset dictionary."""   )
        raise ValueError(
            f'''Dataset at position {i} has at least one split: {list(A_   )}\n'''
            f'''Please pick one to interleave with the other datasets, for example: dataset[\'{next(iter(A_   )   )}\']'''   )
      raise ValueError(
          f'''Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(A_   ).__name__}.'''   )
    if i == 0:
      a_      , a_      :	Union[str, Any]      =							(
          (Dataset, IterableDataset) if isinstance(A_     ,		A_   ) else (IterableDataset, Dataset)
      )
    elif not isinstance(A_     ,		A_   ):
      raise ValueError(
          f'''Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects.'''   )
  if stopping_strategy not in ["first_exhausted", "all_exhausted"]:
    raise ValueError(f'''{stopping_strategy} is not supported. Please enter a valid stopping_strategy.'''   )
  if dataset_type is Dataset:
    return _interleave_map_style_datasets(
        A_     ,		A_     ,		A_     ,		info=A_     ,		split=A_     ,		stopping_strategy=A_   )
  else:
    return _interleave_iterable_datasets(
        A_     ,		A_     ,		A_     ,		info=A_     ,		split=A_     ,		stopping_strategy=A_   )






def 	_snake_case						(      A_       :    List[DatasetType]     ,		A_       :    Optional[DatasetInfo] = None     ,		A_       :    Optional[NamedSplit] = None     ,		A_       :    int = 0     ,		):
  """simple docstring"""







  if not dsets:
    raise ValueError("""Unable to concatenate an empty list of datasets."""   )
  for i, dataset in enumerate(A_   ):
    if not isinstance(A_     ,		(Dataset, IterableDataset)   ):
      if isinstance(A_     ,		(DatasetDict, IterableDatasetDict)   ):
        if not dataset:
          raise ValueError(
              f'''Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} '''
              """is an empty dataset dictionary."""   )
        raise ValueError(
            f'''Dataset at position {i} has at least one split: {list(A_   )}\n'''
            f'''Please pick one to interleave with the other datasets, for example: dataset[\'{next(iter(A_   )   )}\']'''   )
      raise ValueError(
          f'''Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(A_   ).__name__}.'''   )
    if i == 0:
      a_      , a_      :	str      =							(
          (Dataset, IterableDataset) if isinstance(A_     ,		A_   ) else (IterableDataset, Dataset)
      )
    elif not isinstance(A_     ,		A_   ):
      raise ValueError(
          f'''Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects.'''   )
  if dataset_type is Dataset:
    return _concatenate_map_style_datasets(A_     ,		info=A_     ,		split=A_     ,		axis=A_   )
  else:
    return _concatenate_iterable_datasets(A_     ,		info=A_     ,		split=A_     ,		axis=A_   )


