N5: apply systematic listing strategies, including use of the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways)

What are systematic listing strategies?

Ways of writing outcomes from an event in an organised way with none of the possibilities missed out or repeated

How many options are there if, in a meal deal, you can buy a orange or an apple juice with a bacon, cheese or salt flavoured crisps?

OB, OC, OP, AB, AC, AP

6 choices (listed out starting with drinks)

What is the product rule for counting?

A method for finding the total number of ways of selecting items from a set or sets

What are the rules when using product rule for counting

if it says ‘or’, add the possibilities, but ‘and’ means multiply them

Harry is going to a formal event and is choosing what accessories to add to his outfit. He has seven different ties, four different bow ties and five different pairs of cufflinks. How many different ways can Harry get ready if he chooses:

1) Either a tie, a bow tie or a pair of cufflinks?

2) A pair of cufflinks and either a tie or a bow tie?

1) or is used completely here, so add all of the options - 7+4+5=16

2) and and or is used here, so Harry wants a tie and a pair of cufflinks or a bow tie and a pair of cufflinks, which can be written in two ways; CT+CB or C(T+B) - 5×7=35 5×4=20 35+20=55