Six people sit around a circular table. Person A and B must not sit next to each other...how many ways are there of seating them?

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- Nov 14th 2009, 07:33 AMHelenaStageWays of seating people around a circular table
Six people sit around a circular table. Person A and B must not sit next to each other...how many ways are there of seating them?

- Nov 14th 2009, 08:47 AMSoroban
Hello, HelenaStage!

Quote:

Six people sit around a circular table.

Person A and B must not sit next to each other.

How many ways are there of seating them?

With 6 people around a circular table,

. . there are: . ways to seat them.

Duct-tape and together

. . Then we have 5 "people" to arrange: .

There are: . ways to seat them.

But the 5 "people" could be: .

Hence, there are: . ways that andadjacent.*are*

Therefore, there are: . ways in which and areadjacent.*not*

- Nov 14th 2009, 12:21 PMPlato
- Nov 14th 2009, 12:28 PMSoroban
Hello, Plato!

Elegant solution! . . . I like it!