Counting & Combinatorics
Pigeonhole principle, inclusion-exclusion, graph theory basics, and combinatorial arguments
Key Concepts
- Bijections turn a hard count into an easier one
- Invariants and monovariants prove impossibility or termination
- The extremal principle: consider the largest or smallest case
- Double counting evaluates a quantity two different ways
Important Formulae
| Inclusion–exclusion | |A∪B∪C| = Σ|A| − Σ|A∩B| + |A∩B∩C| |
| Handshake lemma | Σ deg(v) = 2 × (number of edges) |
Quick Tips
- Look for an invariant (something that never changes) to prove a task is impossible.
- The extremal principle — picking the maximal/minimal object — cracks many problems.
Sample Practice Questions
-
In how many ways can 2 items be chosen from 4 distinct items?
Show answer
Answer: 6
-
How many subsets does a set with 3 elements have?
Show answer
Answer: 8
-
How many possible outcomes are there when a coin is flipped 3 times?
Show answer
Answer: 8
-
In how many ways can 3 distinct books be arranged in a row?
Show answer
Answer: 6
Practice Questions
Practise RMO questions on Counting & Combinatorics. Answers are revealed after each question.
Start Practice →Frequently Asked Questions
What are the key concepts in Counting & Combinatorics for RMO?
Bijections turn a hard count into an easier one; Invariants and monovariants prove impossibility or termination; The extremal principle: consider the largest or smallest case; Double counting evaluates a quantity two different ways.
Which formulae are important for Counting & Combinatorics in RMO?
Inclusion–exclusion: |A∪B∪C| = Σ|A| − Σ|A∩B| + |A∩B∩C|; Handshake lemma: Σ deg(v) = 2 × (number of edges).
How can I practise RMO Counting & Combinatorics questions for free?
Practise free RMO Counting & Combinatorics questions with instant answers and explanations on Safe Learning for Kids — no sign-up required.