





"""simple docstring"""



from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


a_			=      {
    """configuration_ctrl""": ["""CTRL_PRETRAINED_CONFIG_ARCHIVE_MAP""", """CTRLConfig"""],
    """tokenization_ctrl""": ["""CTRLTokenizer"""],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a_			=      [
           """CTRL_PRETRAINED_MODEL_ARCHIVE_LIST""",
           """CTRLForSequenceClassification""",
           """CTRLLMHeadModel""",
           """CTRLModel""",
           """CTRLPreTrainedModel""",
       ]

try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a_			=      [
           """TF_CTRL_PRETRAINED_MODEL_ARCHIVE_LIST""",
           """TFCTRLForSequenceClassification""",
           """TFCTRLLMHeadModel""",
           """TFCTRLModel""",
           """TFCTRLPreTrainedModel""",
       ]


if TYPE_CHECKING:
       from .configuration_ctrl import CTRL_PRETRAINED_CONFIG_ARCHIVE_MAP, CTRLConfig
       from .tokenization_ctrl import CTRLTokenizer

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_ctrl import (
                  CTRL_PRETRAINED_MODEL_ARCHIVE_LIST,
                  CTRLForSequenceClassification,
                  CTRLLMHeadModel,
                  CTRLModel,
                  CTRLPreTrainedModel,
              )

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_ctrl import (
                  TF_CTRL_PRETRAINED_MODEL_ARCHIVE_LIST,
                  TFCTRLForSequenceClassification,
                  TFCTRLLMHeadModel,
                  TFCTRLModel,
                  TFCTRLPreTrainedModel,
              )

else:
       import sys

       a_			=      _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)











"""simple docstring"""



from math import factorial







def 		__lowercase					(       snake_case_  :  int    ,snake_case_  :  int						)       ->int:



    '''simple docstring'''







    if n < k or k < 0:
        raise ValueError('''Please enter positive integers for n and k where n >= k'''						)
    return factorial(snake_case_						) // (factorial(snake_case_						) * 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.""",
       )




