Stupidest Valentine Problem Ever!

first arrange all alphabetically , AEEILNNTV
then fix a letter and find total words which can be made with it

words with A | 8! / 2! 2! ..........[dividing by 2! 2! because of two N s and E s]
words with E | 8! / 2!
words with I | 8! / 2! 2!
words with L | 8! / 2! 2!
words with N | 8! / 2!
words with T | 8! / 2! 2!

Now with V,
VAE | 6! / 2!
VAI | 6! / 2! 2!
VALEE | 4! / 2!
VALEI | 4! / 2!
VALENE | 3!
VALENI | 3!
VALENN | 3!

VALENT | EIN 1
VALENT | ENI 1
VALENT | IEN 1
VALENT | INE 1

summing all , we get - 81226

Python:

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from itertools import permutations
combos = set()
word = 'valentine'
for combo in permutations(word):
    combos.add(''.join(combo))
combos = list(combos)
combos.sort()
for index in xrange(len(combos)):
    if combos[index] == word:
        break
print "Answer:", index + 1

I used the permutation Method but it is time consuming.

Is there any Shortcut method ?