


"""simple docstring"""







from math import factorial
def _A						(						lowercase	,   lowercase	,   lowercase		):







    """simple docstring"""
    if successes > trials:
        raise ValueError('''successes must be lower or equal to trials'''		)
    if trials < 0 or successes < 0:
        raise ValueError('''the function is defined for non-negative integers'''		)
    if not isinstance(lowercase	,   lowercase		) or not isinstance(lowercase	,   lowercase		):
        raise ValueError('''the function is defined for non-negative integers'''		)
    if not 0 < prob < 1:
        raise ValueError('''prob has to be in range of 1 - 0'''		)
    a					=(prob**successes) * ((1 - prob) ** (trials - successes))
    # Calculate the binomial coefficient: n! / k!(n-k)!
    a					=float(factorial(lowercase		)		)
    coefficient /= factorial(lowercase		) * factorial(trials - successes		)
    return probability * coefficient


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       print("""Probability of 2 successes out of 4 trails""")
       print("""with probability of 0.75 is:""", end=""" """)
       print(binomial_distribution(2, 4, 0.75))



"""simple docstring"""







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


lowerCamelCase_       :       Union[str, Any]      						=  {"""processing_layoutxlm""": ["""LayoutXLMProcessor"""]}

try:
       if not is_sentencepiece_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowerCamelCase_       :       Optional[int]      						=  ["""LayoutXLMTokenizer"""]

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowerCamelCase_       :       Dict      						=  ["""LayoutXLMTokenizerFast"""]

if TYPE_CHECKING:
       from .processing_layoutxlm import LayoutXLMProcessor

       try:
              if not is_sentencepiece_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_layoutxlm import LayoutXLMTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_layoutxlm_fast import LayoutXLMTokenizerFast

else:
       import sys

       lowerCamelCase_       :       Union[str, Any]      						=  _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)