Implement decay simulation and trailing-zero counting

Implement the following in Python: 1) **Radioactive decay simulation:** Half-life is 1 day. Write a simulation function that takes: - input: integer **m** (number of days), integer **n** (number of atoms) - process: simulate independent decay over time (you may model survival each day with probability 0.5, or equivalently sample each atom’s decay time) - output: the final **state** of each particle (e.g., a boolean list/array of length n indicating survived/decayed after m days) and/or the number of survivors. Also discuss runtime and how you would validate correctness against the analytic Binomial(n, 0.5^m) result. 2) **Factorial and trailing zeros:** - (a) Implement a factorial function in Python (mention multiple approaches). - (b) Given an integer **n**, compute the number of trailing zeros in **n!** efficiently (better than computing n! explicitly).