Find the number of distinguishable permutations of the given letters "aaabbbccc".

The answer is:
9!/(1!*3!*3!) 
You take the total quantity of letters you have factorial, divided by each of you dissimilar types of letters factorial. The reason that there is a 1! in the start is since you have the first two A's in the front, so they won't be going anywhere, leaving you with 1 A, therefore, 1!. and there are 3 B and C so 3!