Answer:
each other can be seated in 2 different ways. The remaining 6 plus 1 group of the two persons = 7 entities can be arranged in a circular fashion in (7–1)! =6! ways. Hence total no of ways 8 persons can be seated around a round table such that 2 given persons are seated next to each other = 2*6! = 1440.
the two sitting together can sit two ways, and would be classified as one entity, therefore instead of 8! ways of seating 8 people, there would be 7! x 2 ways of seating 8 people,
(7 x 6 x 5 x 4 x 3 x 2 x 1) x 2 = 10080 ways
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