Write a function that counts how many different ways you can make change for an amount of money, given an array of coin denominations. For example, there are 3 ways to give change for 4 if you have coins with denomination 1 and 2: 1+1+1+1, 1+1+2, 2+2.

coins.py

combinations = []
amount = 12

def count_denoms(denoms, comb):
    global combinations
    for i in range(len(denoms)):
        comb_new = comb + [denoms[i]]
        if sum(comb_new) < amount:
            count_denoms(denoms[i:], comb_new)
        elif sum(comb_new) == amount:
            print(comb_new)
            combinations.append(comb_new)
    
if __name__ == "__main__":
    count_denoms([2, 5, 1], [])
    print("Number of combinations: " + str(len(combinations)))

def count_change(money, coins, ops):
    global combinations
    for i in range(len(coins)):
        _new = ops + [coins[i]]
        if sum(_new) < money:
            count_change(money, coins[i:],_new)
        elif sum(_new) == money:
            print(_new)
            combinations.append(_new)
    
if __name__ == "__main__":
    count_change(4,[2, 1], [])
    print("Number of changes: " + str(len(combinations)))```