1
$\begingroup$

How many ways are there of seating six people at a round table so that two specific people sit together?

I think it is a permuation question but not 100% sure.

Thanks

$\endgroup$
1
$\begingroup$

Hints:

Circular table questions, you can designate one person as "special" and sit them first and arrange everyone else around that person.

"Where a specific group of people must sit together" questions, you can relabel those people as a single unit and then once having arranged everyone else, then having the people in the unit move around in their spot.


For your specific question, you have persons A,B,C,D,E,F. Suppose E and F must sit together. Let them be called X instead. How many ways can you arrange persons A,B,C,D,X around the table? Now, remembering that X is two people, how many ways could E,F be arranged where "X" used to be?

$\endgroup$
  • $\begingroup$ For A,B,C,D,X you can arrange them 5! ways. I'm not sure what you mean for the last part. $\endgroup$ – Jonhy Hubeetto Nov 14 '15 at 23:52
  • $\begingroup$ @JonhyHubeetto You can arrange A,B,C,D,X in $5!$ ways in a line, but not around a circle. For arranging around a circle however we consider ABCDX to be the same arrangement as BCDXA as well as CDXAB, DXABC, and XABCD. So, reiterating what I said earlier, you designate one person as special, say A. You seat them first, and then arrange the rest of the people in the remaining seats. This removes the difficulty of having to deal with the multiple possible representations for the same event. $\endgroup$ – JMoravitz Nov 15 '15 at 1:11
  • $\begingroup$ @JonhyHubeetto So, I'll ask again, how many ways can you arrange A,B,C,D,X around a circle? Now, after having arranged them, decide whether when replacing X by E and F, whether E is on the left or on the right. $\endgroup$ – JMoravitz Nov 15 '15 at 1:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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