Coin Changing Problem

Statement

Given an integer array representing coins of different denominations and an integer amount representing a total amount of money, return the number of ways the coins can sum up to the amount.

There is no limit on the number of coins available to you.

Example

Suppose the available coin denominations are $1$, $2$ and $5$ and the total amount of money is $7$. We can make the change for $7$ in the following six ways: