Systematic Listing & Route Maps explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
Revise the definition, formulae, important results, and exam method first.
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Systematic listing means writing possibilities in an organised order.
It helps you count choices without missing any and without counting the same choice twice.
This is useful in number puzzles, routes, menus, timetables, and probability.
A possibility is one possible answer or outcome.
You have met the idea. Now open a tiny puzzle, a useful fact, and the next best action.
Continue the journey
Route maps show possible paths between places. Each route must follow the allowed connections.
For small problems, listing is helpful because you can see every case. For larger repeated choices, a counting rule may be faster.
Meaning: A systematic list is a list made using a clear order.
Definition: Systematic listing is the method of writing all possibilities without repeats or gaps.
To make twigit numbers from 1, 2, and 3, start with 1: 12, 13. Then start with 2: 21, 23. Then start with 3: 31, 32.
Meaning: A table keeps choices neat.
Definition: A listing table places one choice on rows and another choice on columns.
A table can show all meal choices from starters and drinks.
Meaning: A route map shows possible paths from one place to another.
Definition: A route is one allowed path through a map or network.
If A connects to B and C, and both connect to D, then and are two routes.
Meaning: Sometimes counting is faster than writing every outcome.
Definition: The multiplication principle says total choices can be found by multiplying independent stages of choice.
Easy
Question: List all twigit numbers using 4 and 5 without repeating a digit.
Medium
Question: A student can choose 2 snacks and 3 drinks. How many snacrink pairs are possible?
Exam-level
Question: From A to D, the routes are , , , and . How many routes are listed?
Listing in a random order
Why it happens: A possibility can be missed.
Correct approach: Use a clear order, such as fixing the first digit first.
Counting the same outcome twice
Why it happens: The list is not checked for repeats.
Correct approach: Compare each new outcome with the earlier outcomes.
Using a route that is not connected
Why it happens: The map is not followed carefully.
Correct approach: Move only along allowed lines.
Multiplying when restrictions exist
Why it happens: All choices are assumed to be allowed.
Correct approach: Remove restricted cases or list them directly.
Why not just write answers as I think of them?
A random list can miss cases. A systematic list is easier to check.
When should I use a table?
Use a table when two groups of choices are being matched.
Is systematic listing part of probability?
Yes. It helps count total outcomes and favourable outcomes.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.
If there are 3 shirts and 2 trousers, there are 3 x outfits.