The nine delegates to the Economic Cooperation Conference include $2$ officials from Mexico, $3$ officials from Canada, and $4$ officials from the United States. During the opening session, three of the delegates fall asleep. Assuming that the three sleepers were determined randomly, find the probability that exactly two of the sleepers are from the same country.
The opposite to the qualified event is that the three sleepers are from three different countries or three sleepers coming from the same country. Therefore the answer is $$1-\frac{C_2^1\times C_3^1 \times C_4^1+C_3^3 + C_4^3}{C_{2+3+4}^3}=\boxed{\frac{55}{84}}$$