COMBINATIONS AND PERMUTATIONS. 217 



In dealing a pack of cards, the number of hands, of 

 thirteen cards each, which can be produced is 



52-51-50 ..... 40 



or 635,013,559,600. But in whist four hands are simul- 

 taneously held, and the number of distinct deals becomes 

 so vast that it would require twenty-eight figures to express 

 it. If the whole population of the world, say one hundred 

 thousand millions of persons, were to deal cards day and 

 night, for a hundred million of years, they would not in 

 that time have exhausted one hundred-thousandth part of 

 the possible deals. Now, even with the same hands the 

 play may be almost infinitely varied, so that the complete 

 variety of games which may exist is almost incalculably 

 great. It is in the highest degree improbable that any 

 one game of whist was ever exactly like another, except 

 by intention. 



The end of novelty in art might well be dreaded, did 

 we not find that nature at least has placed no attainable 

 limit, and that the deficiency will lie in our inventive 

 faculties. It would be a cheerless time indeed when all 

 possible varieties of melody were exhausted, but it is 

 readily shown that if a peal of twenty-four bells had been 

 rung continuously from the so-called beginning of the 

 world to the present day, no approach could have been 

 made to the completion of the possible changes* Nay, 

 had every single minute, been prolonged to 10,000 years, 

 still the task would have been unaccomplished. P As 

 regards ordinary melodies, the eight notes of a single 

 octave give more than 40,000 permutations, and two 

 octaves more than a million millions. If we were to take 



' Essay on Probability,' by Lubbock and Drinkwater, Useful Know- 

 ledge Society, 1833, p. 6. 



P Wallis ' Of Combinations/ p. 1 1 6, quoting Vossius . 



