<s>[INST] Balls of 3 colours in a bag - Probability There are $12$ balls in a bag. $3$ of them are red, $4$ of them are green, and $5$ of them are blue. We randomly take out $3$ balls from the bag at the same time. What is the probability that all three balls are of the same colour?
My answer: $(3/12)^3 + (4/12)^3 + (5/12)^3$. Is this correct?
EDIT: My explanation is that since there are the odds of getting a red ball are 3/12, I simply multiplied it 3 times since I consider multiplication to be the "and" operator. Similarly, I consider addition to be the "or" operator. So, the way I think of it is: 
(1 red and 1 red and 1 red) or (1 green and 1 green and 1 green) or (1 blue and 1 blue and 1 blue). 
 [/INST] For $3$ balls of red color $$\mathrm{Prob}=\frac{3}{12}\cdot\frac{2}{11}\cdot\frac{1}{10}$$
For $3$ balls of green color $$\mathrm{Prob}=\frac{4}{12}\cdot\frac{3}{11}\cdot\frac{2}{10}$$
For $3$ balls of blue color $$\mathrm{Prob}=\frac{5}{12}\cdot\frac{4}{11}\cdot\frac{3}{10}$$
Total probability of all ball same color is
$$
\frac{3}{12}\cdot\frac{2}{11}\cdot\frac{1}{10}+\frac{4}{12}\cdot\frac{3}{11}\cdot\frac{2}{10}+\frac{5}{12}\cdot\frac{4}{11}\cdot\frac{3}{10}
$$
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