Hello everybody,

This is probably a simple combinatorics question.

- We do have $\displaystyle A$ red balls, $\displaystyle B$ green balls and $\displaystyle C$ yellow balls ($\displaystyle A, B, C$ is their count, so they are totall $\displaystyle A+B+C$ in count). If we combine them together into $\displaystyle n$-pairs how many are theiruniquecombinations?

I tried for the combination into $\displaystyle 2$-pairs and i solved it for special cases (example $\displaystyle A=3, B=1, C=1$).

$\displaystyle \left(\begin{array}{cc}3\\2\end{array}\right)+

\left(\begin{array}{cc}A-1\\2\end{array}\right)+

\left(\begin{array}{cc}B-1\\2\end{array}\right)+

\left(\begin{array}{cc}C-1\\2\end{array}\right)=4$

However if i try to generalize it, I fail. I know that I am confused and this is probably wrong proccess to the problem.

Thank you all for your time.