In [13]:

    

def get_combinations(amount, denominations):
    combinations = 0
    
    for d in denominations:
        if amount - d > 0:
            combinations += get_combinations(amount - d, denominations)
        elif amount - d == 0:            
            combinations += 1
        
        denominations = denominations[1:]
    
    return combinations


    

In [14]:

    

get_combinations(4, [1, 2, 3])


    

    
Out[14]:





4

In [17]:

    

get_combinations(10, [5, 2, 3])


    

    
Out[17]:





4

In [ ]: