Probability and Combinatorics

What the page covers

The unit splits into two strands that meet in the middle: counting and chance. On the counting side, the Maths Permutations and Combinations mind map sets out when order matters and when it does not, and whether repetition is allowed. The Combinatorics mind map goes further, with compositions, grid walks, domino tilings, Catalan numbers and Fibonacci numbers.

On the chance side, you will find mind maps on mutually exclusive and exhaustive events, independent events, tree diagrams, relative frequency and conditional probability. Notes cover geometric probability and independent and dependent events.

Where to start

1. Begin with the Venn Diagrams flashcards. They cover the universal set, the empty set and what A∩B means.
2. Read the Probability mind maps for the basic language: impossible, unlikely, even chance, likely and certain.
3. Move to the permutation and combination maps, then the tree diagram maps.

Using quizzes and maps together

Read a map first, then take a quiz without looking at it. The Combinations and Permutation quizzes suit counting practice. The Year 8 probability theory quiz and the Math probability test check the basics. Whatever you miss, go back to the matching map and read that branch again.

Going further

Some decks go well beyond school level. The Combinatorics flashcards cover Ramsey numbers and the Erdos and Szekeres theorem. Others cover Markov Chains, Martingales and stochastic integrals. A GCSE Maths module map is also here for school students.

Where it sits

This unit belongs to the Statistics and Probability strand of Mathematics. It leans on counting skills and feeds into wider statistics work.

Choose one map that matches your level, work through it, and see how much a quiz tells you.