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Permutations

 

Arrangements are called permutations.

 

The number of permutation of n different things taken r at a time is
 

   
 

 

Using factorial notations

 

 

   
 

Number of permutations of n things, taken all a time, of which p are alike of one kind, q are alike of 2nd kind, r are alike of third kind and rest are different

   

 

Circular Permutations

 

(i)  The number of circular permutations of n objects = (n – 1)! Because in a circular permutation one thing is kept fixed and the remaining (n – 1) things are arranged in (n – 1)! Ways.  
 

(ii)  If the clockwise and anticlockwise orders are not distinguishable, then the number of ways =       
        

Permutation with restrictions

 

Permutation of n different things when a particular object is not taken in any arrangements is

 

           

 

Permutation of n different things when a particular object is always included in any arrangements is
 

          
 

 





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