162: BE MOIVRE. 



If it be required that some of the Faces marked I, some of 

 the Faces marked ii, and some of the Faces marked ill be 

 thrown, the ProbabiUty required will be 



-f (s-a-hy+ {s-h-cy+{s-c-ay 



— {s — a — h — cy 



And so on if other Faces are required to be thrown. 



De Moivre intimates that these results follow easily from the 

 method adopted in Problem xxxix. 



294. Problem XLII. first appeared in the second edition ; 

 it is not important. 



Problem XLiil. is as follows : 



Any number of Chances being given, to find the Probability of their 

 being produced in a given order, without any limitation of the number 

 of times in which they are to be produced. 



It may be remarked that, for an approximation, De Moivre 

 proposes to replace several numbers representing chances by a 

 common mean value ; it is however not easy to believe that the 

 result would be very trustworthy. This problem was not in the 

 first edition. 



295. Problems XLiv. and XLV. relate to what we have called 

 Waldegrave's Problem ; see Art. 211. 



In De Moivre's first edition, the problem occupies pages 77 — 102. 

 De Moivre says in his preface that he had received the solution 

 by Nicolas Bernoulli before his own was published ; and that both 

 solutions were printed in the PhilosojyJiical Transactions, No. 341. 

 De Moivre's solution consists of a very full and clear discussion 

 of the problem when there are three players, and also when there 

 are four players ; and he gives a little aid to the solution of the 

 general problem. The last page is devoted to an explanation of a 

 method of solving the problem which Brook Taylor communicated 

 to De Moivre. 



In De Moivre's third edition the problem occupies pages 132 — 159. 

 The matter given in the first edition is here reproduced, omitting, 



