In how many ways can they be seated around the table?

[NEHA]

In how many different ways can 6 poker players sit around a circular table?

ok in my view it can be 6!
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Edited by stapel -- Reason for edit: creating intelligible subject line

 

[galactus]

Thay can be seated around a circular table in (n-1)! ways.

 

[NEHA]

so
(n - 1)!
(6 - 1)!
120

 

[daon]

It depends on what the question is asking. If it means how many ways can you seat the children (including which way they're facing) there are 6! ways. If its asking how many ways can you create a seating chart (i.e. who sits next to whom) theres 6!/6 = 5! ways.

In other words, for the first way we would call (1 2 3 4 5 6) different from (2 3 4 5 6 1). In the second way we'd consider them the same since 1 is always between 2 and 6, 3 is always between 2 and 4... etc. Since there are six such permutations we must divide by six.

That was difficult to explain, and I hope it made sense!