There's a bag with 50 balls. 17 white, 10 red, 7 orange, 3 purples 5 yellow, 2 blue and 6 green. We pick 8 balls randomly without putting them back. First, what is the probability of picking exactly 3 white? Second, what is the probability of picking exactly 3 white, 2 red, 1 blue, and 2 green?
I thought of combinotorics to try to solve this but I'm not sure if I'm close or just completely off base. For the first question I had $\frac{\binom{8}{3} \binom{17}{1} \binom{16}{1} \binom{15}{1} \binom{33}{5}} {\binom{50}{8}}$ The top would be the ways to arrange 3 balls among 8 balls, then picking 1 white ball out of 17, then 1 out of 16, then 1 out of 15, then picking 5 balls out of the possible 33 that arent white.
Finally everything divided by the total number of ways to pick 8 balls from 50. I didn't bother trying for question 2 if I hadn't grasped question 1. Am I on the right track here?
Thanks