Permutations and Combinations count arrangements and selections. The factorial $n!=n\times(n-1)\times\cdots\times 1$.
Permutations ($^nP_r$) count ordered arrangements; combinations ($^nC_r$) count selections where order does not matter. For example $5!=120$ and $^4C_2=6$.
Remember
- Permutation = order matters; combination = order doesn't.
- $0!=1$.