Description
Combinations with repetition, binomial theorem, Pascal identity. Shows how counting formulas depend on principles and prior results.
Source: Discrete Mathematics: An Open Introduction; standard combinatorics texts
Dependency Flowchart
Note: Arrows mean "depends on" (tail to head).
graph TD
DefFact("DefFact Factorial")
DefProd("DefProd Product principle")
PermNoRep("PermNoRep Permutations no rep")
CombNoRep("CombNoRep Combinations")
CombRep("CombRep Combinations with rep")
BinomThm("BinomThm Binomial theorem")
Pascal("Pascal Pascal identity")
DefFact --> PermNoRep
DefProd --> PermNoRep
PermNoRep --> CombNoRep
DefFact --> CombNoRep
CombNoRep --> CombRep
CombNoRep --> BinomThm
CombNoRep --> Pascal
classDef axiom fill:#ff6b6b,color:#fff,stroke:#c0392b
classDef definition fill:#b197fc,color:#fff,stroke:#9775fa
classDef theorem fill:#51cf66,color:#fff,stroke:#40c057
class DefFact,DefProd definition
class PermNoRep,CombNoRep,CombRep,BinomThm,Pascal theorem
Color Scheme
Red
Axioms
Axioms
Blue
Definitions
Definitions
Teal
Theorems
Theorems
Statistics
- Nodes: 7
- Edges: 7
Keywords
- combinatorics
- permutations
- combinations
- binomial theorem
- counting