Algebraic Formulas

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


     Recurence formula of permutations:




     , or
     Recurence formula of arrangements:



  Recurrence formulas of Combinations:

     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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