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from operator import mul
from functools import reduce

from itertools import permutations

def factorial(n):
    return reduce(mul, range(1,n+1), 1)

def word_index(word):
    index = 1
    alpha = sorted(word)
    for letter in word:
        order = alpha.index(letter)
        order1 = sorted(list(set(alpha))).index(letter)
        del alpha[order]
        left = len(alpha)
        repeats = left - len(set(alpha))
        index += (factorial(left)/factorial(repeats)) * order1
    return index

def index_choices(iterable):
    s = sorted(iterable)
    l = []
    for i in iterable:
        index = s.index(i)
        l.append(index)
        del s[index]
    return l

if __name__ == '__main__':
    words = 'abab aaab baaa question bookkeeper nonintuitiveness'.split()
    expected = [2, 1, 4, 24572, 10743, 8222334634]

    # words = permutations('a b c d'.split())
    # expected  = range(reduce(mul, range(2,5), 1))
    for word, exp in zip(words, expected):
        act = word_index(word)
        print('{word} exp:{exp} act:{act} {result}'.format(word=word, exp=exp,
              act=act, result='PASS' if exp == act else 'FAIL'))