Calcular las combinaciones de una lista

Un concepto matemático modelado con recursión

def factorial(n):
    if n <= 1:
        return 1
    return n * factorial(n-1)

def how_many_combinations(n, r):
    return factorial(n) / (factorial(n -r)*factorial(r))

def calc_combination(items, r, len, start_from):    
    take = r - 1    
    for i in range(start_from, len - take): 
        if r == 1:
            yield [items[i]]
        else:
            item = items[i]
            for j in calc_combination(items, r-1, len, i + 1):
                yield [item] + j

def combination(items, r):
    return calc_combination(items, r, len(items), 0)

if __name__ == '__main__':
    print(a, b)
    data = ['A', 'E', 'I', 'O', 'U']
    group = 3
    gen = combination(data, group)
    n = how_many_combinations(len(data), group)
    print(f"The number of combinations are: {n}")
    while True:
        try:
            print(next(gen))
        except StopIteration:
            break```