Trace Coin Change II with coins [1,2,5] and amount 5. The key is loop order: coins in outer loop to count combinations (not permutations). Let dp[a] = number of ways to make amount a. After coin 1: dp[1..5]=1 (only one way using just 1s). After coin 2: dp[2]=2, dp[3]=2, dp[4]=3, dp[5]=3. After coin 5: dp[5]=4.
Answer: 4 ways. They are: [1,1,1,1,1], [1,1,1,2], [1,2,2], [5].