PERMUTATION AND COMBINATION. 235 



PROBLEM VI. 



21? find the numher cf combinations of any given number of 

 things, by taking any given number at a time ; in ivhith 

 ^fy^ are several things of one scrty several cf another , C3*c. 



RULE. 



1. Find, by trial, the number of difFerent forms, which 

 .the things, to be taken at a time, will admit of, and the num- 

 ber of combinations in each. 



2. Add together all the combinations, thus found, and 

 the suln will be the number required. 



EXAMPLES. 



I. Let the things proposed be aaabhc ; it is required to 

 find the number of combinations that can be made of every 

 -three of these quantities. 



Forms. Combinatioas. 



1 a'^by a*Cf b^a^ b^c 4 



abc I 



6 = number of combina- 



.tions required. 



2. Let qaahbbcc be proposed j it Is required to find the 

 number of combinations of these quantities, taken 4 at a 

 time. 



Ans. 10. 



3. How many combinations are there in aaaabbccde, 8 

 being taken at a time ? 



Ans. 13. 



4. How many combinations are there in aaaaabhbhhccccdd 

 ddecfcfffg, \ o being taken at a time ? 



Ans. 2819. 



PROBLEM 



