
'''simple docstring'''
import math

a_											=						10
a_											=						7
a_											=						BALLS_PER_COLOUR * NUM_COLOURS

def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE = 2_0       ):
    """simple docstring"""






    snake_case_ :    Optional[Any]     			=						math.comb(__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       )
    snake_case_ :    int     			=						math.comb(NUM_BALLS - BALLS_PER_COLOUR,		__SCREAMING_SNAKE_CASE       )

    snake_case_ :    Optional[Any]     			=						NUM_COLOURS * (1 - missing_colour / total)

    return f'{result:.9f}'


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






'''simple docstring'''
import doctest
from collections import deque

import numpy as np






class    UpperCAmelCase_				:





 def __init__(    self):
     snake_case_ :    List[Any]     			=						[2, 1, 2, -1]
     snake_case_ :    int     			=						[1, 2, 3, 4]





 def        snake_case__		(    self):
     snake_case_ :    str     			=						len(self.first_signal)
     snake_case_ :    Any     			=						len(self.second_signal)

     snake_case_ :    List[Any]     			=						max(lowercase_ ,       lowercase_)

     # create a zero matrix of max_length x max_length
     snake_case_ :    Dict     			=						[[0] * max_length for i in range(lowercase_)]

     # fills the smaller signal with zeros to make both signals of same length
     if length_first_signal < length_second_signal:
         self.first_signal += [0] * (max_length - length_first_signal)
     elif length_first_signal > length_second_signal:
         self.second_signal += [0] * (max_length - length_second_signal)
     for i in range(lowercase_):
         snake_case_ :    List[str]     			=						deque(self.second_signal)
         rotated_signal.rotate(lowercase_)
         for j, item in enumerate(lowercase_):
             matrix[i][j] += item

        # multiply the matrix with the first signal
     snake_case_ :    Any     			=						np.matmul(np.transpose(lowercase_) ,       np.transpose(self.first_signal))

     # rounding-off to two decimal places
     return [round(lowercase_ ,       2) for i in final_signal]


if __name__ == "__main__":
  doctest.testmod()




