Permutations & Combinations

The problem, from first principles

01-random-variables's Binomial PMF leaned on binom{n}{k}, "n choose k," without deriving it, this question fills that gap by building the two counting tools every discrete-probability formula eventually needs: permutations (how many ways to arrange k items out of n, where order matters, who finishes 1st/2nd/3rd in a race) and combinations (how many ways to choose k items out of n, where order doesn't matter, who's on a 3-person committee). Every discrete distribution built from "count the favorable outcomes, divide by total outcomes", Binomial, Hypergeometric, Multinomial, starts here.

From theory to code

Implement permutations_count(n, k) and combinations_count(n, k), using Python's math.factorial. The signatures and docstrings are already in the editor.

Constraints

• n and k are non-negative integers with 0 <= k <= n.
• Use math.factorial, already imported in the starter.

Hints