If all 7 letters were distinguishable, the answer would be 7!
But since the 3 A's are not distinguishable, 3! of the 7! look alike, so we divide by 3!, and get 7!/3!
Since the 2 T's are not distinguishable, 2! of the 7!/3! look alike, so we also divide by 2!
Answer:
Edwin
You can put this solution on YOUR website!
There are letters, so there are ways in arranging } objects into spaces.
But we've overcounted by a factor of ('s can interchange in ways), and ('s can interchange in ways).
To better understand this concept, let's name each repeated letter:
Now, we can rearrange Atlanta to make:
Without the superscripts, we make Atlanta.
But, we've already made that word with:
This is because we need to account for the times the's can change and we wouldn't notice, and the 's can change and we won't notice.
Thus, our final number of ways becomes:
different ways
