COMBINATIONS AND PERMUTATIONS. 199 



that concur in producing a given event, or effect, is 

 oftentimes so immensely great, and the causes them- 

 selves are so different one from another, that it is ex- 

 tremely difficult to reckon up all the different ways in 

 which they may be arranged or combined together, it 

 often happens that men, even of the "best understandings 

 and greatest circumspection, are guilty of that fault in 

 reasoning which the writers on logic call the insufficient 

 or imperfect enumeration of parts or cases : insomuch 

 that I will venture to assert, that this is the chief, and 

 almost the only, source of the vast number of erroneous 

 opinions, and those too very often in matters of great 

 importance, which we are apt to form on all the subjects 

 we reflect upon, whether they relate to the knowledge of 

 nature or the merits and motives of human actions. It 

 must therefore be acknowledged, that that art which 

 affords a cure to this weakness, or defect, of our under- 

 standings, and teaches us so to enumerate all the possible 

 ways in which a given number of things may be mixed 

 and combined together, that we may be certain that we 

 have not omitted any one arrangement of them that can 

 lead to the object of our inquiry, deserves to be con- 

 sidered as most eminently useful and worthy of our 

 highest esteem and attention. And this is the business 

 of the art or doctrine of combinations. Nor is this art 

 or doctrine to be considered merely as a branch of the 

 mathematical sciences. For it has a relation to almost 

 every species of useful knowledge that the mind of man 

 can be employed upon. It proceeds indeed upon mathe- 

 matical principles, in calculating the number of the com- 

 binations of the things proposed : but by the conclusions 

 that are obtained by it, the sagacity of the natural 

 philosopher, the exactness of the historian, the skill and 

 judgment of the physician, and the prudence and fore- 

 sight of the politician maybe assisted ; because the business 



