rERMUTATlON AND COMBINATION. 223 



cd at last 2I. IS. 8d. : how many days did he work, and 

 how many was he idle ? 



Ans. He wrought 30 days, and was idle 10. 



5, A gentleman has two horses of considerable- value, 

 and a saddle worth 50I. ; now, if the saddle be put on the 

 back of the first horse, it will make his value double that 

 of the second ; but if it be put on the back of the sec- 

 ond, it will make his value triple that of the first : what 

 is the value of each horse ? 



Ans. One 30I. and the other 40L 



6. There is a fish, whose head is 9 inches long, and his 

 tail is as long as his head and half as long as his body, and 

 his body is as long as his tail and his head '. what is the 

 whole length of the fish ? Ans. 3 feet* 



PERMUTATION and COMBINATIOR 



The Permutation of ^tantittes is the shewing how many 

 different ways the order or position of any given number 

 of things may be changed. 



This is also called Variation^ Aliernatttm^ or Changes ; 

 and the only thing to be regarded here is the order they 

 stand in ; for no two parcels are to have all their quanti- 

 ties placed in the same sitaation. 



The Combination of ^lantiiies is the shewing how often 

 a less number of things can be taken out of a greater, and 

 combined together, without considering their places, or the 

 order they stand in. 



This is sometimes called Election, or Choite ; and here 

 every parcel must be different from ail the rest, and no two 

 are to have precisely the same quantities, or things. 



The Compcsiiion of ^mniitles is the taking a given num- 

 b^er of quantities out of as many equal rows of different 



quantities, 



