# Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

Combinatorics has several approaches and subfields that include: counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).

vCalc's Combinatorics library contains equations cutting across several sub-fields of combinatorics.

### Parent Categories:

## Combinatorics Calculators

## Combinatorics Equations

- Circular Permutations
- Circular r-Permutation of n Elements
- Combinations C(n,k)
- Combinations with Repetitions
- Conditional Probability of B given A
- factorial
- Gamma Function
- Permutations
- Permutations with repetition
- Prime Number Theorem
- Stirling's Formula
- 1 to 31
- Circular r-Permutation of n elements
- Comparison Permutations
- Count of Combinations (nCr)
- Law of Total Probability P(A+B)
- Permutations nPr
- Powerball Chances
- Probability of A and B
- Probability of A or B
- Probability of Flush losing (fraction)
- Probability of Flush losing (percentage)
- Probability of Four of a Kind losing (fraction)
- Probability of Four of a Kind losing (percentage)
- Probability of Full House losing (fraction)
- Probability of Full House losing (percentage)
- Probability of High Card losing (fraction)
- Probability of High Card losing (percentage)
- Probability of Non-independent Events (A, B)
- Probability of One Pair losing (fraction)
- Probability of One Pair losing (percentage)
- Probability of Royal Flush losing (fraction)
- Probability of Royal Flush losing (percentage)
- Probability of Straight Flush losing (fraction)
- Probability of Straight Flush losing (percentage)
- Probability of Straight losing (fraction)
- Probability of Straight losing (percentage)
- Probability of Three of a kind losing (fraction)
- Probability of Three of a kind losing (percentage)
- Probability of Two Pair losing (fraction)
- Probability of Two Pair losing (percentage)
- Stirling Numbers

## Combinatorics Constants

- five card hands
- Powerball Possibilities
- Probability of Flush (fraction)
- Probability of Flush (percentage)
- Probability of Four of a Kind (fraction)
- Probability of Four of a Kind (percentage)
- Probability of Full House (fraction)
- Probability of Full House (percentage)
- Probability of One Pair (fraction)
- Probability of One Pair (percentage)
- Probability of Royal Flush (fraction)
- Probability of Royal Flush (percentage)
- Probability of Straight (fraction)
- Probability of Straight (percentage)
- Probability of Straight Flush (fraction)
- Probability of Straight Flush (percentage)
- Probability of Three of a Kind (fraction)
- Probability of Three of a Kind (percentage)
- Probability of Two Pair (fraction)
- Probability of Two Pair (percentage)