Example 3. A pocket contains 7 white balls and 3 black balls of the same size. If two balls are drawn at random, what is the probability of getting one white ball and one black ball? (Exercise 6, Question 6)
From 7 white balls and 3 black balls, any 2 balls can be drawn with $\mathrm{C}_{10}^{2}$ equally possible outcomes, among which the outcomes of getting one white and one black ball are $\mathrm{C}_{7}^{1} \cdot \mathrm{C}_{3}^{1}$, so the required probability is
$$
\frac{\mathrm{C}_{7}^{1} \cdot \mathrm{C}_{3}^{1}}{\mathrm{C}_{10}^{2}}=\frac{7}{15}
$$