

'''simple docstring'''

from __future__ import annotations

import math


def    A_  ( snake_case      ,       snake_case ):
  SCREAMING_SNAKE_CASE:Optional[Any]						      =					u
  for i in range(1      ,       __UpperCAmelCase ):
    SCREAMING_SNAKE_CASE:Dict						      =					temp * (u - i)
  return temp


def    A_  ( ):
  SCREAMING_SNAKE_CASE:Union[str, Any]						      =					int(input("enter the numbers of values: " ) )
  SCREAMING_SNAKE_CASE:List[Any]						      =					[]
  for _ in range(__UpperCAmelCase ):
    y.append([] )
  for i in range(__UpperCAmelCase ):
    for j in range(__UpperCAmelCase ):
      y[i].append(__UpperCAmelCase )
      SCREAMING_SNAKE_CASE:List[Any]						      =					0

  print("enter the values of parameters in a list: " )
  SCREAMING_SNAKE_CASE:Any						      =					list(map(__UpperCAmelCase      ,       input().split() ) )

  print("enter the values of corresponding parameters: " )
  for i in range(__UpperCAmelCase ):
    SCREAMING_SNAKE_CASE:List[str]						      =					float(input() )

  SCREAMING_SNAKE_CASE:int						      =					int(input("enter the value to interpolate: " ) )
  SCREAMING_SNAKE_CASE:str						      =					(value - x[0]) / (x[1] - x[0])

  # for calculating forward difference table

  for i in range(1      ,       __UpperCAmelCase ):
    for j in range(n - i ):
      SCREAMING_SNAKE_CASE:Any						      =					y[j + 1][i - 1] - y[j][i - 1]

  SCREAMING_SNAKE_CASE:Union[str, Any]						      =					y[0][0]
  for i in range(1      ,       __UpperCAmelCase ):
    summ += (ucal(__UpperCAmelCase      ,       __UpperCAmelCase ) * y[0][i]) / math.factorial(__UpperCAmelCase )

  print(F'''the value at {value} is {summ}''' )


if __name__ == "__main__":
    main()









'''simple docstring'''

from math import factorial





def    A_  ( snake_case      ,       snake_case ):

  # If either of the conditions are true, the function is being asked
  # to calculate a factorial of a negative number, which is not possible
  if n < k or k < 0:
    raise ValueError("Please enter positive integers for n and k where n >= k" )
  return factorial(snake_case ) // (factorial(snake_case ) * factorial(n - k ))


if __name__ == "__main__":
    print(
        "The number of five-card hands possible from a standard",
        f'''fifty-two card deck is: {combinations(52, 5)}\n''',
    )

    print(
        "If a class of 40 students must be arranged into groups of",
        f'''4 for group projects, there are {combinations(40, 4)} ways''',
        "to arrange them.\n",
    )

    print(
        "If 10 teams are competing in a Formula One race, there",
        f'''are {combinations(10, 3)} ways that first, second and''',
        "third place can be awarded.",
    )






