Letter Tile Possibilities

You have tiles with letters. How many different non-empty sequences can you form using the tiles? Each tile can be used once per sequence, but sequences can be of any length.

Examples
Input: "AAB"
Output: 8
Hints

Letter Tile Possibilities

You have tiles with letters. How many different non-empty sequences can you form using the tiles? Each tile can be used once per sequence, but sequences can be of any length.