10. A bag contains 10 balls each of red, white, and black colors. If 12 balls are drawn from it, but it is required that all three colors are included, then there are $\qquad$ different ways to do so.
10. 55 Consider the generating function $f(t)=\left(t+t^{2}+\cdots+t^{10}\right)^{3}=t^{3} \frac{\left(1-t^{10}\right)^{3}}{(1-t)^{3}}$, obviously we only need to consider the coefficient of $t^{9}$ in the expansion of $(1-t)^{-3}$, which is $C_{2+3-1}^{2}=C_{11}=55$.