Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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).

share|improve this question
    
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
1  
Technically Finns are not Scandinavians) –  Alex Oct 24 '12 at 19:25
add comment

1 Answer 1

They sit AROUND a table. Think about the case with only two persons.

share|improve this answer
    
Oh, I see now. thanks –  the_enigma Oct 24 '12 at 17:28
    
Good. The seating is invariant under rotation. –  M.B. Oct 24 '12 at 17:29
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.