We use systematic listing to list all of the possible outcomes of an event or all the possible combinations. Listing in a systematic way helps to make sure we do not miss any possible outcomes.
Example 1: Here is a restaurant menu.
List all the possible combinations of one main and one dessert.
We can start by picking the first main, Pizza. If we pick Pizza, we then have 3 options for dessert.
Pizza and Cheesecake
Pizza and Crumble
Pizza and Ice Cream
We now have all the possible options involving pizza, so we can move on to the next main:
Pasta and Cheesecake
Pasta and Crumble
Pasta and Ice Cream
And finally we can list all options with the third main:
Burger and Cheesecake
Burger and Crumble
Burger and Ice Cream
We have now listed all the possible options for one main and one dessert.
Example 2: Here are three number cards:1 7 5
Write down all the possible two-digit numbers that can be made with these cards.
We can start with all the numbers with 1 in the tens
17 and 15
Next we can list all the numbers with 7 in the tens
71 and 75
Finally we can have 5 in the tens
51 and 57
We have now listed all the possible two-digit numbers.