Combinatorics Fundamentals
Core counting principles and combinatorial formulas.
The data
0
- Principle
- Product Rule
- Description
- If task A has m ways and task B has n ways, both can be done in m * n ways.
- Formula
- m * n
1
- Principle
- Sum Rule
- Description
- If tasks are mutually exclusive with m and n ways, total is m + n.
- Formula
- m + n
2
- Principle
- Permutations
- Description
- Ordered arrangements of r elements from n items.
- Formula
- P(n,r) = n! / (n - r)!
3
- Principle
- Combinations
- Description
- Unordered selections of r elements from n items.
- Formula
- C(n,r) = n! / (r!(n-r)!)
4
- Principle
- Permutations with Repetition
- Description
- Arrangements when some elements are identical.
- Formula
- n! / (n1! * n2! * ... * nk!)
5
- Principle
- Pigeonhole Principle
- Description
- If n items are placed into m containers and n > m, some container has >= 2 items.
- Formula
- ceil(n/m)
6
- Principle
- Binomial Theorem
- Description
- Expansion of (a + b)^n.
- Formula
- (a+b)^n = Sum C(n,k) * a^(n-k) * b^k
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