PERMUTATION AND COMBINATION. 23 1 



4. Join the first letter to every one of the twos follow- 

 ing it, and the second, third, &c. as before i and it will 

 give the combinations of all the threes. 



5. Proceed in the same manner to get the combinations 

 of all the fours, &c. and you will at last get all the sev- 

 eral forms of combination, and the number in each form. 



EXAMPLES. 



I. How many changes may be made of every 4 letters, 

 that can be taken out of these 6, aaabbc ? 



No. of Forms. No. of com- No. of changes in 



forms. binations. each form. 



X2X3X4=24 

 isfc a^li, a'^c 2 -l — =4. 



X2X3 =6 



2d a'h 



1: 



1.1X2X1X2=4 



r 1x2x3x4=24 



i ~=i2. 



LIX2 =2 



3d a^hc, b'^ae 2 



4X2= 8 



6X1= 6 



12X2=24 



38 = the number of changes required. 



2. How many changes can be made of every 8 letters 

 out of these 10, aaaahhccde ? 



Ans. 22260. 



3. How many different numbers can be made out of i 

 unit, 2 twos, 3 threes, 4 fours, and 5 fives, taken 5 at a 

 time ? 



Ans. 21 1 1. 



PROBLEM 



