LeetCode 518 Coin Change II - Combinations vs Permutations

Consider coins $[1, 2]$ and amount $3$. The combinations are: $[1,1,1], [1,2]$. That's $2$ ways. But if you count $[1,2]$ and $[2,1]$ separately, you get $3$ ways. The naive approach: for each amount, try all coins.

This counts permutations because you might add coin 1, then coin 2, OR coin 2, then coin 1. The fix: for each coin, update all amounts. This keeps you process coins in a fixed order. Once you've "moved past" a coin, you never go back to it. That's what makes combinations work.