import math
def fact(n: int) -> int:
return math.factorial(n)
def fact_zero(n: int) -> int:
# factorial(0) == 1.
return math.factorial(n)
def binomial(n: int, k: int) -> int:
# n choose k = n! / (k! * (n-k)!) — exercises factorial in arithmetic.
return math.factorial(n) // (math.factorial(k) * math.factorial(n - k))