Python script to count the number of ways letters in a string (passed in as argument) can be rearranged

Letter_Permutations.py

# USAGE: python Letter_Permutations.py <string here>
#        Do not put spaces between multiple words in the string

import argparse
import math

# Reads word from argument
parser = argparse.ArgumentParser()
parser.add_argument('word', help = "Word to count combinations for")
args = parser.parse_args()

# Converts all letters to lowercase for consistency
word = (args.word).lower()

# Numerator of final formula
wordLength = len(word)
numerator = math.factorial(wordLength)

# List containing all letters of the word
wordArray = list(word)

# Number of times each letter occurs stored in list
letterOccurances = list()
# List of letters that have been counted in wordArray
countedLetters = list()

# Loops through wordArray, counts how many times a letter occurs, skips over
# already counted letters using a list of such letters (list updated each time) 
for letter in wordArray:
    if letter in countedLetters:
        continue
    letterOccurances.append(wordArray.count(letter))
    countedLetters.append(letter)

# Denominator of final formula
denominator = 1
for i in letterOccurances:
    denominator = (denominator * math.factorial(i))

# Result
print "Number of permutations: " + str(numerator/denominator)