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Circular seating arrangements

Published online by Cambridge University Press:  20 April 2012

D. S. Jones  and
P. G. Moore
D. S. Jones
Affiliation:
University of Dundee and London Business School
P. G. Moore
Affiliation:
University of Dundee and London Business School
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Extract

This problem concerns n couples around a circular table, husbands and wives seated alternately. The number of ways in which the n couples can be seated such that no husband and wife sit next to each other is required. This problem is not covered in the standard texts such as Feller (1950) or Whitworth (1901) who concentrate on the simpler linear problem, i.e. seating arrangements in a row. In this paper we obtain a solution for the circular problem, deriving thereby the probability that no such matching occurs when the seating is made at random, and showing finally that this probability has a limiting value when n is large.

Type
Other
Information
Journal of the Institute of Actuaries , Volume 108 , Issue 3 , December 1981 , pp. 405 - 411
Copyright
Copyright © Institute and Faculty of Actuaries 1981

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References

Feller, W. (1950). An introduction to probability theory and its applications. Wiley, Chapman & Hall.Google Scholar
Whitworth, W.A. (1901) Choice and chance (5th edn). Hafner Publishing Company.Google Scholar