

'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available


lowerCamelCase			:				Dict 			=					{}


try:
     if not is_sentencepiece_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowerCamelCase			:				Union[str, Any] 			=					["MLukeTokenizer"]

if TYPE_CHECKING:
     try:
          if not is_sentencepiece_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_mluke import MLukeTokenizer


else:
     import sys

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



'''simple docstring'''
from math import factorial


def 	_lowerCAmelCase (						_UpperCamelCase						:					int							,			_UpperCamelCase						:					int							,			_UpperCamelCase						:					float    )				->      float:
     """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(_UpperCamelCase							,			_UpperCamelCase    ) or not isinstance(_UpperCamelCase							,			_UpperCamelCase    ):
          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'    )
     _SCREAMING_SNAKE_CASE							   =(prob**successes) * ((1 - prob) ** (trials - successes))
     # Calculate the binomial coefficient: n! / k!(n-k)!
     _SCREAMING_SNAKE_CASE							   =float(factorial(_UpperCamelCase    )    )
     coefficient /= factorial(_UpperCamelCase    ) * 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, 0.7_5))
