Probability

Total number of ways$= {}^{12}C_3 = \frac{12!}{3! \times 9!} = 220$Number of ways to draw exactly 2 red balls and 1 non-red ball$= {}^{4}C_2 \times {}^{8}C_1 = 6 \times 8 = 48$Number of ways to draw exactly 2 green balls and 1 non-green ball$\; = {}^{5}C_2 \times {}^{7}C_1$$\; = \frac{5!}{2! \times 3!} \times \frac{7!}{1!6!} = 10 \times 7 = 70$Number of ways to choose 2 white balls from 3.$= {}^{3}C_2$Number of ways to draw exactly 2 white balls and 1 non-white ball$\; = {}^{3}C_2 \times {}^{9}C_1 = \frac{3!}{2! \times 1!} \times \frac{9!}{1!8!}$$\; = 3 \times 9 = 27$Total number of ways to draw exactly 2 balls of the same colour$= 48 + 70 + 27 = 145$∴ Required probability $= \frac{145}{220} = \frac{29}{44}$