234- ARITHMETIC. 



EXAMPLES. 



I. How ms^ny combinations can Be -matlc of 6 lefteris^ 



out of 10? 



1X2K3X4X5X 6(=: the number to be taken at a time)= 720 

 10x9x8 X 7 X6X5(= same number from 10)3=151200 

 720)151200(210 t^e answer-. 

 1440 



720 



720 



^. How many combinations can tie Tha& cr£ 2 letfer^j- 

 out of 24 letters of the alphabet I 



An Si 276.^ 



3.- A general, who hacT often been successful in \^ar,- 

 was asked by his King, what reward he should confer upon' 



him for his servieoa y the general only desired a farthihg 



for every file, of 10 men in a file, which he could make^ 

 with a body of 100 men : what is the amount in pound* 



sterling ? 



Ans. 1 303 15723 50I. 9s. 2d. 



PROELEJ-f- 



Burthe smn of this series is = HyJILJ vJ^^Ill y which 13- 



I 2 3 



the same as the rule. 



And the same thing wii! hold, let the number of things, to be 

 taken at a time, be what it may ; therefore the number of com* 



binations of m tilings, taken n at a time, will == — X— ^ X~ ■ 



123, 



y,^^^, &c. to n terms. Q^ E. P. 

 4 



