PER 



Coiribinations, 



1. The number ot combination* that can be formed out of n thing 1 .*, 



Taken 2 and '.<. together ?/. - 



?/ _ i _ o 

 \\ and 3 w. 



?' and ; 



Thus how mauy combinations can be made of t\vo letters out of the 26 

 letters of the alphabet, 



2. The total number of combinations of n things taken 1 and 1 ; 2 and 

 2 j 3 and 3, &c. together, 



Thus all the possible combinations that can be made of a common suit 

 of 13 cards taking them by one's, two's, three's, c. at a time = 2 1 

 = 8191. 



3. All the possible permutations and combinations that any number of 

 things can be made to undergo when taken by two's, three'.-?, ike., up to 

 the whole number of things given, is expressed by the sum of the geo- 

 metrical scries n -f >/ 2 -f- ifi -f- n* ............ -f n 1 ; and .'. 



nn _ ] 

 * nt^T X * 



Thus the whole number of permutations and combinations that can be 

 made of the 1 letters a, b, c, d, when they are taken by two's, three's, 

 and four's 



4. Supposing there are m sets of things, one set containing n things, 

 another p t another 7, &c., then the total number of combinations that 

 can be formed by taking one from each 6et 



n X P X q ......... to m factors. 



Thus suppose there are 4 companies, in one of which there are tS men, 

 in another 8, in each of the other two .0, then the number of changes 

 that can be made by taking one out of each company = 68. n. t> = L>8SS. 

 204 



