2019
Problem - 4385
A child builds towers using identically shaped cubes of different colors. How many different towers with a height of $8$ cubes can the child build with $2$ red cubes, $3$ blue cubes, and $4$ green cubes? (One cube will be left out.)
The answer is $\boxed{1260}$. This is because arrangements of $8$ blocks have a bijective relation with those of $9$ blocks by simply removing the last block. Meanwhile, the number of arrangements of $9$ blocks can be computed as $$\frac{9!}{2!\cdot 3!\cdot 4!}=\boxed{1260}$$