Question 151446
your answer seems low


the 3 together are a single position, leaving 7 other positions
__ putting 8 things in 8 positions (order counts) 8P8 or 8!


with the round table, each arrangement is repeated 8 times
__ with the difference being the "starting point" position
__ if the only concern is who is next to who, then the number of arrangements is reduced by a factor of 8 to 7!


the 3 together can also have different arrangements
__ 3 things in 3 positions (order counts) 3!


so the answer should be the product of 7! and 3!