Two students X and Y are best friends. They sit randomly in a row of 9 seats with 7 other friends to watch a movie. What is the probability that the friends sit together?

Taking X and Y as one pair, we can have 8 people on 8 seats. These 8 elements can be seated in 8! ways and X and Y can be seated in 2! ways. Therefore, the total number of ways X and Y can be seated together are 2!8!
Total number of ways 9 people can be seated is 9!

The probability that X and Y will be seated together is $$\frac{2!8!}{9!}=2\times\ \frac{8!}{9\times\ 8!}=\frac{2}{9}$$
Therefore, Option C is the correct answer.