Product-Rule-For-Counting Aqa Higher

Product rule for counting

What is meant by counting principles?

• Counting principles state that if there are m ways to do one thing and n ways to do another there are m × n ways to do both things

• Applying counting principles allows us to …

  • … see patterns in real world situations

  • … find the number of combinations or arrangements of a number of items

  • … find the number of ways of choosing some items from a list of items

• When you have a question like “How many ways…?” you should always look for the words “AND” and “OR”

  • “AND means ×” 
    “OR means +”

How do I choose an item from a list of items AND another item from a different list of items?

• If a question requires you to choose an item from one list AND an item from another list you should multiply the number of options in each list

  • In general if you see the word ‘AND’ you will most likely need to ‘MULTIPLY’

• For example if you are choosing a pen and a pencil from 4 pens and 5 pencils:

  • You can choose 1 item from 4 pens AND 1 item from 5 pencils

  • You will have 4 × 5 different options to choose from

How do I choose an item from a list of items OR another item from a different list of items?

• If a question requires you to choose an item from one list OR an item from another list you should add the number of options in each list

  • In general if you see the word ‘OR’ you will most likely need to ‘ADD’

• For example if you are choosing a pen or a pencil from 4 pens and 5 pencils:

  • You can choose 1 item from 4 pens OR 1 item from 5 pencils

  • You will have 4 + 5 different options to choose from