A Sum In Permutations

The Yale lock manuacturers have proved that in a patent loek having six "steps," each capable of being reduced in height twenty times, the number of changes or combinations will be 80,400. Further, that as the drill pin and the pipes of the keys may be made of three different sizes, the total nurnber of changes will be 2,592,000. In keys f the smallest size the total number ef changes through which they can be , run is 648,600, while in those of large the number can bo increased to not less than 7,776,000 difïereat changea. This is not so surprising when we flnd on turning up an arithmetic book thut the number of changes that can b rang on twenty-four bells is 620448,01,733,239,439,360,000.