A group of 18 Scandinavians consists of $5$ Norwegians, $6$ Swedes, and $7$ Finns. They are seated at random around a table. Compute the following probabilities:
(a) that all the Norwegians sit together,
(b) that all the Norwegians and all the Swedes sit together, and
(c) that all the Norwegians, all the Swedes, and all the Finns sit together.
For (b) I don't understand why this is different from (c)?
If all Norwegians and all the Swedes sit together then wouldn't that mean that whatever seats left are going to be filled by the Fins?
therefore shouldn't the answer be $\frac {2!7!5!6!}{17!}$
I don't understand why the answer given for part be is $\frac {8!6!5!}{17!}$