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A Note on Restricted Selections

Published online by Cambridge University Press:  11 August 2014

M. T. L. Bizley
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Extract

In a recent note (Bizley, 1960) the writer described a device which simplifies the solution of certain derangement problems. The present note explains and illustrates another device in combinatorial work (and hence in probability) having potentialities that do not seem to be well known. It is useful in tackling problems concerned with the choice of objects from an array when restrictions are placed upon the relative positions of those to be chosen, and it has applications to runs of consecutive events.

Type
Research Article
Information
Journal of the Staple Inn Actuarial Society , Volume 16 , Issue 5 , November 1961 , pp. 333 - 345
Copyright
Copyright © Institute of Actuaries Students' Society 1961

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References

REFERENCES

Bizley, M. T. L. (1950) A note on the variance-ratio distribution. J.S.S. 10, 62.Google Scholar
Bizley, M. T. L. (1957 a). Probability: An Intermediate Text-book. Cambridge University Press.Google Scholar
Bizley, M. T. L. (1957 b). A further table of binomial coefficients. J.S.S. 14, 326.Google Scholar
Bizley, M. T. L. (1960). A note on some elementary derangement and allied problems. J.S.S. 16, 147.Google Scholar
Burr, E. J. (1961). Problem no. 4963. Amer. math. Mon., 68, 383.Google Scholar
Macmahon, P. A. (1915, 1916). Combinatory Analysis. (2 vols.) Cambridge University Press.Google Scholar
Riordan, J. (1958). An Introduction to Combinatorial Analysis. New York: Wiley.Google Scholar