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Combinations 

 

Groups or selections are called combinations
 

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

 

 

 (

 


 

Properties of

 

(i)

 

(ii)       

 

 


 

Combination of n different things taking some or all of n things at a time is-

           

      2n – 1

    

The combinations of selecting r1  things from a set having n1, objects and r2 things from a set having n2 objects where combination of r1 things, r2 things are independent is given by

 

      

 

 


 

Cor. 1  The number of ways in which (p + q + r) things can be arranged into three groups containing p, q and r things respectively is

 

       


 

 



 

Cor.2   The number of ways in which 3p things can be divided equally into three distinct groups is

     

         

 

 

 

 


 

 

Cor.3  The number of ways in which 3p things can be divided equally into three persons is

 

 

 

 

 

 

 





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