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10 people are having dinner at a circular table. They sit down, eat their starter and then stand up. In how many ways can they now sit down to eat their main so each person has a different neighbour to the right?

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  • $\begingroup$ So define ji to be the ith person is sat next to the original right neighbour. Define the union of all ji, from one to ten. This is equal to j1+j2+....j10 -j1intersectj2 -j1j3.... equal to 10 by8! -10c2 *7!..... Then do 1- this? $\endgroup$ – grigori Oct 25 '16 at 16:43
  • $\begingroup$ sorry i don't know how to do the latex $\endgroup$ – grigori Oct 25 '16 at 16:48
  • $\begingroup$ Put equations in between $ signs and _ just before indices, you will eventually need to add brackets { } More detail here $\endgroup$ – Astyx Oct 25 '16 at 16:53

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