THE INDUCTIVE OR INVERSE METHOD. 277 



by some person acquainted with the usual order of 

 sequence. This conclusion is quite irresistible, and rightly 

 so ; for there are but two suppositions which we can make 

 as to the reason of the cards being in that particular 

 order : 



1. They have been intentionally arranged by some one 

 who would probably prefer the numerical order. 



2. They have fallen into that order by chance, that is, 

 by some series of conditions which, being wholly unknown 

 in nature, cannot be known to lead by preference to the 

 particular order in question. 



The latter supposition is by no means absurd, for any 

 one order is as likely as any other when there is no prepon- 

 derating tendency. But we can readily calculate by the 

 doctrines of permutation the probability that fifty-two 

 objects would fall by chance into any one particular order. 

 Fifty-two objects can be arranged in 



52x5ix5Ox.... x4x3x2xior 8066 x (io) 64 

 possible orders, the number obtained requiring 68 places 

 of figures for its full expression. Hence it is excessively 

 unlikely, and, in fact, practically impossible, that any one 

 should ever meet with a pack of cards arranged in perfect 

 order by pure accident. If we do meet with a pack so 

 arranged, we inevitably adopt the other supposition, that 

 some person having reasons for preferring that special 

 order, has thus put them together. 



We know that of the almost infinite number of possible 

 orders the numerical order is the most remarkable ; it is 

 useful as proving the perfect constitution of the pack, and 

 it is the intentional result of certain games. At any rate, 

 the probability that intention should produce that order is 

 incomparably greater than the probability that chance 

 should produce it; and as a certain pack exists in that 

 order, we rightly prefer the supposition which most 

 probably leads to the observed result. 



