The Counting Principle
Grade 7 Math Worksheets
The basic counting principle states that if there are X ways to do one thing, and Y ways to do another, then there are X × Y ways of doing both.
Similarly, if there are X ways to do one thing, and Y ways to do second one and Z ways to do third one, then there are X × Y × Z ways of doing all the three.
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The Counting Principle states that we multiply the number of choices to find the total number of possibilities.
So, number of ways Daniel can choose the kites = 6 × 4 = 24 ways
Example: Isabelle wants to order frozen yoghurt. If there are 5 different flavours of yoghurt and 14 different toppings to choose from, then in how many different ways can Isabelle place her order?
Number of ways Isabelle can place her order = 5 × 14 = 70 ways
Check Point
- Sandy wants to buy flowers for his friend. There are 5 colors of roses, 4 colors of lilies, and 2 types of orchids. In how many ways can Sandy choose 3 flowers of each type?
- A kitchen garden shop has 6 types of floral plants and 12 plants of different vegetables. Hebrew wants to buy one floral plant and one plant from vegetables. In how many ways can he choose the 2 plants?
- Shawna’s doll has 6 different dresses, 5 sandals and 4 colors of hairs, which are detachable and can be replaced. In how many ways can Shawna dress up her doll?
- Millie’s grandmother bought 2 types of bread and made 4 types of fillings for sandwiches. In how many different ways can her grandmother make sandwiches?
- Peter has 6 shirts, 3 neck ties and 4 trousers for a party. In how many ways can he dress up himself?
Answer key
- 40 ways
- 72 ways
- 120 ways
- 8 ways
- 72 ways
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