Answer : Option A

Explanation :

Total number of balls = 3 + 5 + 4 = 12
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 12 = ¹²C₃
Let E = Event of drawing 3 different coloured balls
To get 3 different coloured balls,we need to select one black ball from 3 black balls,
one red ball from 5 red balls, one blue ball from 4 blue balls
Number of ways in which this can be done = ³C₁ × ⁵C₁ × ⁴C₁
i.e., n(E) = ³C₁ × ⁵C₁ × ⁴C₁

$MF#%\text{P(E) = }\dfrac{\text{n(E)}}{\text{n(S)}}$MF#%$MF#%= \dfrac{3_{C_1} \times 5_{C_1} \times 4_{C_1}}{12_{C_3}}$MF#%

$MF#%= \dfrac{3 \times 5 \times 4 }{\left(\dfrac{12 \times 11 \times 10}{3 \times 2 \times1}\right)}
= \dfrac{3 \times 5 \times 4 }{2 \times 11 \times 10}
= \dfrac{3 \times 4 }{2 \times 11 \times 2}
= \dfrac{3 }{11}$MF#%