A company with n employees publishes an internal calendar, where each day lists the employees having a birthday that day. What is the probability that there is at least one day in the year when nobody has a birthday? (a) 0)) (C) (d) Start as follows: 1. What is the probability of a xed person not having a birthday on a xed day? 2. What is the probability of every person not having a birthday on a xed day? 3. What is the probability of at least one person having a birthday on a xed day? Continuing with this approach will lead you to a plausible, somewhat accurate, but incor- rect answer. Give that answer and explain why it is incorrect. This time, consider the birthday assignment as partitioning of birthdays into subsets or distributing balls into boxes. Conth https : / len .wikipedia. org/Hi kilTwelvefold_way#Formulas to compute the num- ber of ways to assign birthdays in the required fashion. (Pay attention to whether our items and buckets are distinguishable or not.) Give the answer to the original problem. Give a Python simulation to compute the empirical answer to the problem. You now have three answers: crude from (a), exact from (b), and empirical from (c). Plot all three for n from 0 to 5000 with a step of 100. if the numbers grow too big for Python to handle, switch to mpz, add, mul, and bincoef from https :l/gmpyZ. readthedocs . iol