# 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 **k **elements equal **C**_{n}^{k}.

*For a = b = 1,* we get

.

**Note.** The number of subsets of set with **n **items is **2**^{n}.

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

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