Question:
A bag contains $5$ white and $4$ black balls and another bag contains $7$ white and $9$ black balls . A ball is drawn from the first bag and two balls are drawn from the second bag. What is the probability of drawing one white and two black balls?
My Approach:
Case $1$: 1 white ball from bag $1$ and $2$ balls from bag $2$ . So probability is $$\frac{\binom{5}{1}\times \binom{9}{2}}{\binom{9}{1}\times\binom{16}{2}}$$
Case $2$: I can't understand how to solve this part.