Systematic listing means generating every possible outcome of a situation in an organised order, so that nothing is missed and nothing is counted twice. It matters because it's the groundwork for probability: you can't find $P(\text{event})$ correctly without first knowing the total number of possible outcomes.

Fix the first item from one group, pair it with every item from the second group, then move to the next item in the first group and repeat.

Example: 3 number cards (5, 2, 8) are used to form two-digit numbers, no digit repeated.

• Fix 5: 52, 58
• Fix 2: 25, 28
• Fix 8: 85, 82

This gives all 6 possible numbers with no omissions. Notice that order matters here (52 and 25 are different), whereas choosing 2 vegetables from a set would not require both orderings — the method naturally tells you which applies based on what you're being asked to list.

When two events combine (two dice, two spinners, a coin and a die), a grid is more reliable than a list: label one event's outcomes across the top, the other's down the side, and fill each cell with the combined result.

Multiply the number of choices in each group — this is the product rule for counting — and compare it to how many outcomes you actually listed. If the numbers don't match, re-check for a duplicate or a missing combination.

Example: 3 drinks and 2 snacks give $3 \times 2 = 6$ total combinations; two spinners with 3 and 4 sections give $3 \times 4 = 12$.

Put the items in a fixed order (usually numerical or alphabetical) and work through them one at a time, never jumping back to an earlier item once you've moved past it — this single rule is what stops both duplicates and omissions.

Example: list all 2-digit numbers less than 40 using the digits 1, 3, 4 (no repeats). Working through the tens digit in order — 1, then 3 — gives 13, 14, 31, 34. The tens digit can't be 4, since that would make the number 40 or more.

Spinner A has sections scored 1, 2, 3. Spinner B has sections scored 1, 2, 3, 4. The score is the product of the two spinners. Complete a table showing all possible scores, and state how many of the 12 outcomes give a score greater than 6.

Scores greater than 6: $8, 9, 12$ — that's 3 outcomes out of 12.