Given $26$ balls - $8$ yellow, $7$ red and $11$ white - how many ways are there to select $12$ of them? I'm interested in knowing and  understanding the solution to the following problem: 
given $26$ balls - $8$ yellow, $7$ red and $11$ white - how many ways are there to select $12$ of them (all balls of the same colour are indistinguishable).
I've read something about generating functions but I hoped there was a more straightforward way to "see" the solution...I really can't figure it out.
Thanks in advance for your help!

Multiply $\displaystyle(1+x +...+x^8)(1+x+..+x^7)(1+x+..+x^{11})$, and the coefficient of $x^{12}$ of this product is your answer. 
