How many anagrams are there of the word " $A B R A C A D A B R A$ "? And for any given word?
We have 11! permutations of the 11 letters of this word (11! ways to reorder them). However, some of these permutations give the same anagram. Indeed, for each anagram, we can permute the 5 "A", the 2 "B", and the 2 "R". Thus, we count $5! \times 2! \times 2!$ times the same anagram. Therefore, we have: $\frac{11!}{5!2!2!}=83160$ different anagrams possible.