Find all possible combinations of $A, A, A, B, B$ 10 year old daughter has this problem.
She knows that all possible combinations of $A,B,C,D$ are $4! = 24  $
She figured it like this:
If I write down $A$ first, it has $4$ possible places.
If I write down $B$ next, it has $3$ possible places for each of the places of $A (4.3)$
If I write down $C$ next, it has $2$ possible places for each of the above placings $(4.3.2)$
If I write down $D$ last, it has $1$ possible place for each of the above placings $(4.3.2.1)$  
How can she extend this method to find out all possible combinations of $A,A,A,B,B$ ?

Hint. 
First pretend that the $A$'s and $B$'s are actually different - for example, say they're numbered $A_1$, $A_2$, $A_3$, $B_1$, $B_2$. Then this is the same problem you mentioned, and there are $5!$ ways to arrange the letters.
The problem is that you'll obtain many arrangements that differ only because of the numbering. So your problem is to determine how many arrangements there are differing only by the numbering that correspond to a single arrangement where the numbering is ignored.
For example, how many arrangements including numbers correspond to ABAAB? Can you get this by a calculation?
