Coin Change II

Statement

Suppose you are given a list of coins and a certain amount of money. Each coin in the list is unique and of a different denominationA denomination is a unit of classification for the stated or face value of financial instruments such as currency notes or coins.. You are required to count the number of ways the provided coins can sum up to represent the given amount. If there is no possible way to represent that amount, then return 0.

Note: You may assume that for each combination you make, you have an infinite number of each coin. In simpler terms, you can use a specific coin as many times as you want.

Let's say you have only two coins, $10$ and $20$ cents, and you want to represent the total amount of $30$ cents using these coins. There are only two ways to do this, you can use either of the following combinations:

• 3 coins of $10$ cents: $10+10+10=30$.

• 1 coin of $10$ cents and 1 coin of $20$ cents: $10+20=30.$

Constraints:

• 1 <= coins.length <= 300

• 1 <= coins[i] <= 5000

• All the coins have a unique value.

• 0 <= amount <= 5000

Examples

Let's see a few more examples to get a better understanding of the problem statement: