Product Rule For Counting Worksheet

Product rule for counting at a glance

The product rule for counting is a way of working out how many different possible outcomes there are for two or more events. The product rule states that the total number of outcomes of two or more events is equal to the number of different outcomes for each separate event multiplied together. For example, if a restaurant serves 3 starters, 6 main courses and 2 desserts, the total number of ways of choosing a starter, main course and dessert would be 3 ✖ 6 ✖ 2 = 36. 

If we are asked to list all of the possible outcomes when two or more events occur, it is best to use a systematic listing strategy. This helps us to ensure we list all of the possible combinations and avoid duplication. 

There are many real life contexts for using the product rule for counting, especially with security. A standard padlock usually has four wheels, each with the digits 0 to 9. This means that there are 10 different outcomes for each wheel. For four wheels, we would multiply 10 by itself 4 times (written as 104 when using indices). Evaluating this number means that there are 10,000 different combinations for a standard padlock. 

Looking forward, students can then progress to additional probability worksheets, for example the combined events probability worksheet, the relative frequency worksheet, or the describing probability worksheet.

For more teaching and learning support on probability our GCSE maths lessons provide step by step support for all GCSE maths concepts.