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 $A,A,A,B,B$ ?

There are $5!$ combinations of $A_1A_2A_3B_1B_2$ if we first assume the $A$'s and $B$'s to be distinct. In all these combinations $A_1, A_2$ and $A_3$ can appear in $3!$ different ways, but they would all give the same word, so we'll have to divide by $3!$. Given the same argument for $B_1$ and $B_2$ we have to divide once again with $2!$, so the answer would be $\frac{5!}{3!2!}$.
