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An alternative approach to a problem by A. de Moivre

Published online by Cambridge University Press:  23 January 2015

Aristides V. Doumas
Aristides V. Doumas*
Affiliation:
Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece e-mail: [email protected]
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Extract

Suppose n (fair) dice each having m faces marked with numbers 1 to m, are thrown at random. The problem of determining the number of ways in which the sum of the numbers exhibited by the dice will be equal to a given number k has a very long history. In particular, the three dice problem (i.e. the case where m = 6, n = 3), goes back to the 13th century (see [1]). Later, it was Cardano and Galileo who solved it (see [2, 3]). The general case was stated without proof in A. de Moivre's first work on probability, De Mensura Sortis, (1712, p.220). De Moivre was the first who published a proof (using generating functions) in Miscellanea Analytica (1730, p. 196). Furthermore, Montmort had also the solution (via inclusion-exclusion) by 1713, and independently of De Moivre (see [4, 2]).

Type
Articles
Information
The Mathematical Gazette , Volume 97 , Issue 540 , November 2013 , pp. 446 - 454
Copyright
Copyright © The Mathematical Association 2013

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