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Combined events can be shown in different ways such as by systematic listing, or by using tables, grids, Venn diagrams and tree diagrams. The probability of a particular combined event can then be found.

At Higher GCSE, you might also use the product rule.

Systematic listing

The outcomes for an event can be listed in an organised or systematic way to make sure that none of the possible outcomes is missed out. Look for patterns to help find all the outcomes.

Example

How many different three-digit numbers can be made using the digits 3, 6, and 9?

First, find all the numbers that can start with 3:

• 369 and 396

There will also be two numbers that start with 6 and 9:

• 639 and 693
• 936 and 963

So there are six possible numbers:

• 369
• 396
• 639
• 693
• 936
• 963