






from math import pow, sqrt






def   UpperCamelCase  (       *snake_case__     :   float  ):




     '''simple docstring'''






     __snake_case			:Optional[int]          =						len(snake_case__  ) > 0 and all(value > 0.0 for value in values  )
     return result






def   UpperCamelCase  (       snake_case__     :   float	,snake_case__     :   float  ):




     '''simple docstring'''






     return (
         round(sqrt(molar_mass_a / molar_mass_a  )	,6  )
         if validate(snake_case__	,snake_case__  )
         else ValueError("""Input Error: Molar mass values must greater than 0."""  )
     )






def   UpperCamelCase  (       snake_case__     :   float	,snake_case__     :   float	,snake_case__     :   float  ):




     '''simple docstring'''






     return (
         round(effusion_rate * sqrt(molar_mass_a / molar_mass_a  )	,6  )
         if validate(snake_case__	,snake_case__	,snake_case__  )
         else ValueError(
             """Input Error: Molar mass and effusion rate values must greater than 0."""  )
     )






def   UpperCamelCase  (       snake_case__     :   float	,snake_case__     :   float	,snake_case__     :   float  ):




     '''simple docstring'''






     return (
         round(effusion_rate / sqrt(molar_mass_a / molar_mass_a  )	,6  )
         if validate(snake_case__	,snake_case__	,snake_case__  )
         else ValueError(
             """Input Error: Molar mass and effusion rate values must greater than 0."""  )
     )






def   UpperCamelCase  (       snake_case__     :   float	,snake_case__     :   float	,snake_case__     :   float  ):




     '''simple docstring'''






     return (
         round(molar_mass / pow(effusion_rate_a / effusion_rate_a	,2  )	,6  )
         if validate(snake_case__	,snake_case__	,snake_case__  )
         else ValueError(
             """Input Error: Molar mass and effusion rate values must greater than 0."""  )
     )






def   UpperCamelCase  (       snake_case__     :   float	,snake_case__     :   float	,snake_case__     :   float  ):




     '''simple docstring'''






     return (
         round(pow(effusion_rate_a / effusion_rate_a	,2  ) / molar_mass	,6  )
         if validate(snake_case__	,snake_case__	,snake_case__  )
         else ValueError(
             """Input Error: Molar mass and effusion rate values must greater than 0."""  )
     )










import math

lowerCamelCase__							=     10
lowerCamelCase__							=     7
lowerCamelCase__							=     BALLS_PER_COLOUR * NUM_COLOURS






def   UpperCamelCase  (       snake_case__     :   int = 20  ):




     '''simple docstring'''






     __snake_case			:Dict          =						math.comb(snake_case__	,snake_case__  )
     __snake_case			:int          =						math.comb(NUM_BALLS - BALLS_PER_COLOUR	,snake_case__  )

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

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


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


