Combinations and Permutations

Combinations ($nC_k$) and Permutations ($nP_k$) are fundamental concepts in combinatorics.

• Permutations (order matters): $nP_k = \frac{n!}{(n-k)!}$
• Combinations (order doesn't matter): $nC_k = \frac{n!}{k!(n-k)!}$

Key identities include $nC_k = nC_{n-k}$ and $\frac{nP_k}{nC_k} = k!$. It is also helpful to memorize factorials up to 10! for speed.