Choosing K Items with Recursion

Include/exclude branch reduces to binomial structure; prune when picks left exceed remaining.

Try this in Python

import itertools

print(len(list(itertools.combinations(range(5), 2))))

Key takeaways

• Memoize (i, k_left) for speed.
• Symmetry: C(n,k)=C(n,n-k) for bounds.
• Iterative DP often safer for depth.