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!

Let $y,r,w$ denote the number of yellow balls, red balls and so on... Then you need to find the number of solutions to the following equation
$$y+r+w=12 \qquad \text{ with } 0 \leq y \leq 8, 0 \leq r \leq 7, 0 \leq w \leq 11.$$
Can you proceed from here?
