Let $A, B,$ and $C$ be the respective events that the first, second, and the third drawn orange is good.

Therefore, probability that first drawn orange is good, $\mathrm{P}(\mathrm{A})=\frac{12}{15}$

The oranges are not replaced.

Therefore, probability of getting second orange good, $\mathrm{P}(\mathrm{B})=\frac{11}{14}$

Similarly, probability of getting third orange good, $\mathrm{P}(\mathrm{C})=\frac{10}{13}$

The box is approved for sale, if all the three oranges are good.

Thus, probability of getting all the oranges good $=\frac{12}{15} \times \frac{11}{14} \times \frac{10}{13}=\frac{44}{91}$

Therefore, the probability that the box is approved for sale is $\frac{44}{91}$.