How many distinguishable 7 letter "words" can be formed using the letters in alabamaalabama?

You are given the word alabama and you are asked to find how many distinguishable 7 letter "words" can be formed from it.

ALABAMA has seven letters so we will start at 7! 
Counting the number of A's in the word we have 4 A's and so we will divide it by 4!
Counting the number of L's in the word we have 1 L and so we will divide it by 1!
Counting the number of B's in the word we have 1 B and so we will divide it by 1!
Counting the number of M's in the word we have 1 M and so we will divide it by 1!

And so the number of ways is 7! / (4! x 1! x 1! x 1!) = 210 words.