I have an exercise in combinatorics:
There are $6$ white balls, $8$ red balls, $4$ yellow balls and $6$ black balls. In how many ways can I pull $6$ balls?
Is it possible to solve it with the multinomial coefficient? I just started reading about them in Harris/Hirst/Mossinghoff's Combinatorics and Graph Theory and I sense it's possible, It appears that it would be possible, but I sense that it would be a little overkill.
It seems that if I take: $\displaystyle{6 \choose w,r,y,b}$, then I'd have to assign combinations for $w,e,y,b$, like taking first: $\displaystyle{6 \choose 6,0,0,0}$ and then $\displaystyle{6 \choose 5,1,0,0}$ and then $\displaystyle{6 \choose 5,0,1,0}$ and continuing through this process (this is what I meant with overkill). The book seems to tell me that there is a simpler way, but I'm not sure.