2. A bag contains 5 red balls, 6 black balls, and 7 white balls, all of the same size and shape. Now, 14 balls are drawn at random. The probability of drawing exactly 3 red balls is $\qquad$ .
2. $\frac{13}{51}$.

When 14 balls are drawn from a bag of 18 balls, the number of ways to draw is $\mathrm{C}_{18}^{14}$, among which the number of ways to draw exactly three red balls is $\mathrm{C}_{5}^{3} \mathrm{C}_{13}^{11}$. Therefore, the required probability is
$$
P=\frac{\mathrm{C}_{5}^{3} \mathrm{C}_{13}^{11}}{\mathrm{C}_{18}^{14}}=\frac{13}{51} .
$$