Algebraic Formulas

Combinatorics: Permutations. Arrangements. Combinations. Newton's Binomial theorem

Permutations

    
     Recurence formula of permutations:
        

 

 

Arrangements

     , or
         
     Recurence formula of arrangements:
        

Combinations

    

or
     
  Recurrence formulas of Combinations:
        
Demonstration:
    

     Formula complementary combinations:
        

 


 

Newton's Binomial Theorem

    Formula Newton's binomial theorem is:
      
     Termenul general al dezvoltarii binomului lui Newton:
      
     We notice that,

     Finding the highest rank within the development (a + b)n is done by formula
      

     Note. For a set with n items the number of subsets with elements equal Cnk.

     For a = b = 1, we get

.

 

     Note.  The number of subsets of set with n items is 2n.

Keywords: algebra, combinatorics elements, permutations, arrangements, combinations, Newton binomial theorem

 

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