Factorial & Binomial Expansion
The problem, from first principles
"How many ways can you arrange n distinct items in a row?" and "how many ways can you pick k items out of n, where order doesn't matter?" are two of the most common counting questions in probability — and both have short, closed-form answers built directly out of 02-product-notation's ∏. This question implements both, since the second (the binomial coefficient) is exactly what the Binomial distribution later in this track counts with.
From theory to code
Implement factorial(n) first, then n_choose_k(n, k) in terms of it. The signatures and docstrings are already in the editor.
Constraints
nandkare non-negative integers, with0 <= k <= nforn_choose_k.factorial(0) == 1(the empty-product convention from02-product-notation).- Return integers, not floats, even though the intermediate division in
n_choose_kcould otherwise produce one.
Hints
Hint 1
factorial(n) is ∏_{i=1}^{n} i — the exact same accumulate-by-multiplying loop as 02-product-notation's product, just written out directly here rather than imported (every question's solution.py is self-contained).
Hint 2
Use integer division (//) for the final division in n_choose_k, since the numerator is always exactly divisible by the denominator for valid n/k — the result is a count, and counts are integers.
Keywords
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