AP ICET 2017 Shift 1 Paper

Total number of balls $=9+6=15$
Total number of ways 3 balls can be drawn out of 15 balls ${=}^{15}{\mathit{C}}_3=\frac{15\times 14\times 13}{6}$
Number of ways 1 red ball can be drawn out of 9 red balls $=9{\mathit{C}}_1=9$
Number of ways 2 white balls can be drawn out of 6 white balls ${=}^6{\mathit{C}}_2=\frac{6\times 5}{2}=15$
∴ Required probability $=\frac{9\times 15}{\left(\frac{15\times 14\times 13}{6}\right)}=\frac{27}{91}$