Counting and combinations

How many outfits, codes, teams or lottery tickets are there? Counting them one by one is slow and easy to get wrong. This topic builds, step by step, the clever ways to count without listing, from tidy lists and tree diagrams up to Pascal's triangle and the binomial theorem.

Step	Page	You will be able to
Play	How many ways?	Count outfits, handshakes and arrangements with tidy lists and tree diagrams
Explore	The multiplication principle	Count codes, menus and routes by multiplying, and know when to add instead
Build	Permutations	Use factorials to count arrangements, including letters that repeat and seats round a table
Master	Combinations and Pascal's triangle	Count groups where order does not matter and read the answers off Pascal's triangle
Beyond	The binomial theorem	Multiply out any power of a bracket, and prove facts by counting the same thing two ways