Evaluating formula for math.SE batched coupon collector problem

chocolates.py

# https://math.stackexchange.com/questions/3278200/box-of-10-chocolates/3278285

from math import factorial
from fractions import Fraction

def binom(n,k): # binomial coefficient n choose k
  return 0 if n < k else factorial(n)/factorial(k)/factorial(n-k)

def e(n,m): # expected number of days to replace all n chocolates if replaced m at a time
  return binom(n,m)*sum(Fraction(pow(-1,s+1)*binom(n,s),binom(n,m)-binom(n-s,m)) for s in range(1,n+1))

e(10,3) # Fraction(8241679, 911064)