^24 ARITHMETIC. 



quantities, one out of each row, and combining them to-^ 

 gether. 



Here no regard is had to their places ; and it differs 

 from combination only, as that admits of but one row, or 

 set, of things. 



Cotnbhiations of the same form are those, in which there 

 is the same number of quantities, and the same repeti- 

 tions : thus, ahccy bbady deef Sec. are of the same form ; 

 but Mcy abbhy aaccy &c. are of different forms. 



PROBLEM I. 



u^o find the number of permutations ^ or changes y that can be 

 made of any given number of things^ all different from 

 each other. 



RULE.* 



Multiply all the terms of the natural series of numbers^ 



from I up to the given nnmher, r^oiT-tinually together, and 



the last product will be the answer required. 



EXAMPLES. 



* The reason of the rule may be shewn thus : any one thing a 

 is capable only of one position, as a. 



Any two things^ a and 3, are only capable of two vaiiations j 

 as abi la ; whose number is expressed by 1X2. 



If there be 3 things, ^, b and r, then any two of them, leaving 

 out the third, will have 1x2 variations ; and consequently, when 

 the third is taken in, there will be 1x2x3 variations. 



In the same manner, when there are 4 things, every 3, leaving 

 out the fourth, will have 1X2X3 variations. Then, the fourth 

 being taken in, there will be 1X2X3X4 variations. And so 0% 

 as far as you pleaje. 



