【Analysis】 $10+9+1=20$ (only) ; The worst-case scenario is taking 19 balls, just without any red balls. Taking one more will do.
Second Part (8 points per question, total 40 points)
6. A box contains 10 black balls, 9 white balls, and 8 red balls. If you close your eyes and draw balls from the box, how many balls must you draw to ensure that you have at least one red ball and one white ball? $\qquad$