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This is a good example of a very poorly specified question. There are four correct answers which depend on conditions which are unspecified in the question. The chairs can be in a line or around a table (in a crude circle); and in each case you can be interested only in who is sitting next to whom (or a vacant chair) but not really interested on whether it is to the right or left (so that mirror images are counted as the same).


  • chairs are in a line and the direction does matter, then there are 2520.
  • chairs are in a line and the direction does not matter, then there are 1260.
  • chairs are in a circle and the direction does matter, then there are 360.
  • chairs are in a circle and the direction does not matter, then there are 180.
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7y ago

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Q: How many ways can 5 people sit in 7 chairs?
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