



def        lowercase_							(A : int = 1_0		,					A : int = 2_2      ):
       snake_case__							:	Optional[int]   	=	range(1		,					A      )
       snake_case__							:	Optional[int]   	=	range(1		,					A      )
       return sum(
           1 for power in powers for base in bases if len(str(base**power      )      ) == power      )


if __name__ == "__main__":
 print(F"""{solution(10, 22) = }""")











from math import factorial
def        lowercase_							(A : int		,					A : int		,					A : float      ):
       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(A		,					A      ) or not isinstance(A		,					A      ):
              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'      )
       snake_case__							:	List[Any]   	=	(prob**successes) * ((1 - prob) ** (trials - successes))
       # Calculate the binomial coefficient: n! / k!(n-k)!
       snake_case__							:	List[str]   	=	float(factorial(A      )      )
       coefficient /= factorial(A      ) * 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))






