# Permutations of three groups of people

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.

I understand how to setup the numerators in all these cases, however the solution says the sample space is 17! as apposed to the 18! factorial I thought it would be (since there are 18 people in total).

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This is a round table, with $17$ ordinary chairs and a throne. Without loss of generality you can seat the shortest Finn on the throne. –  André Nicolas Oct 24 '12 at 17:31
Technically Finns are not Scandinavians) –  Alex Oct 24 '12 at 19:25