We have $8$ blue balls that are numbered $\{1,2,3,4,5,6,7,8\}$. We have $8$ red balls that are numbered $\{1,2,3,4,5,6,7,8\}$.
I think it should be ${8 \choose 5}\cdot 2^5$.
There ${8 \choose 5}$ is as choosing $5$ distinct digits from $\{1,2,3,4,5,6,7,8\}$ and $2^5$ is as choosing the color either blue or red for the balls we chose.
Is my thinking correct? Any suggestions or corrections?