SOLUTION: In how many ways can 10 people be seated at a round table if 3 of them sit next to each other? my answer is 10080. is it correct?

Question 151446: In how many ways can 10 people be seated at a round table if 3 of them sit next to each other?
my answer is 10080. is it correct?
Found 2 solutions by scott8148, Ali-aithzaz:
Answer by scott8148(5885) (Show Source):
You can put this solution on YOUR website!
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!

Answer by Ali-aithzaz(4) (Show Source):
You can put this solution on YOUR website!
Since 10 people are sitting in round table, we have to fix one of them, 9 left then three are sitting next to each other, they will act as a unit so ways when those 9 will sit 6! , and the three can sit 3! Ways,
so total arrangement when 10 people sit arround a table when 3 sit next to each other is 3!*6!