Hindoo Rules of Arithmetic. 147 



Lastly, it is evident that i.2-3...n is the number of permutations of n 

 different things ; but if feveral fets of figures are alike, as r figures of one., 

 kind, s figures of another, for inftance ; then let (1.3.3. ..n):(l.2..r) x (l»2...s) 

 &c. the number of permutations in that cafe be called N; then the Sum of 

 the permutations is N: n x (a + b + c + ...n) x (1 11... n) in general. 



EXAMPLE. Required the Sum of the permutations of 1 1335 * 



i.a.3-4-5 = ?o; ¥. = 6; 6x10 = 78; 78 



i.a.i.s S w * ' 



78 

 78 

 78 

 78 



866658 the Sum required. 



T 2 



