--- title: "Systematic Listing" description: "Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)" canonical: https://lightmysky.com/learn/mathematics/systematic-listing-mt_gu0NPDvlhY source: https://lightmysky.com/learn/mathematics/systematic-listing-mt_gu0NPDvlhY.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Systematic Listing Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options) Subject: Mathematics · Area: Algebra · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/systematic-listing-mt_gu0NPDvlhY ## Ready when they can - List all possible meal combinations from 3 starters and 4 mains - Organise combinations into a systematic table to ensure none are missed - Explain why the total number of combinations equals the product of the options in each category ## Lesson: Listing every combination A combination is one choice from each group, put together. If you have 3 T-shirt colours and 2 trouser colours, each outfit combines one shirt colour with one trouser colour. To list every combination without missing any, go through the colours in order instead of guessing. *(drawing: Each row is a shirt colour. Each column is a trouser colour. Every cell in the grid is one outfit, so there are 3 x 2 = 6 outfits in total.)* **Example.** A cafe offers 3 starters and 4 mains. Pick the first starter and pair it with each of the 4 mains. Then move to the second starter and pair it with each main again. Keep going until every starter has been paired with every main. This gives 3 x 4 = 12 meal combinations. **Tip.** Work through one group in order, pairing each item with every item in the other group before moving on. This systematic method stops you skipping a pair or writing the same one twice. **Recap.** List combinations one group at a time, and the total always equals the two group sizes multiplied together. ## Practice 16 questions on this page, each with its working shown. ## Needs first - [Long multiplication (age 10+)](https://lightmysky.com/learn/mathematics/long-multiplication-age-10-mt_XLP1IM3Qbb) ## Opens up - [Counting Outcomes with the Product Rule](https://lightmysky.com/learn/mathematics/counting-outcomes-with-the-product-rule-mt_74gSbYIG8p)